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When it's math, not music...

It comes down to learning the material, rather than trying to remember it.

Simple way is to chart it out.
No bass involved, the instrument is not needed, as it is not a playing issue that is physical, it is a playing issue that us mental.

"If you can say it you can play it." was what i was taught, the idea is that if you chart out and understand the arrangement you simple play what you learned from it.

Now this is a cool way to learn a song deeper, so here is an example to try.

Take any song you can play and without listening to it, or using an instrument to play it, write down its arrangement by bars.

So points to include are intro;
Do all the instruments come in together or do the build in to song?
When does the 1st verse actually start, does it start with the vocals or is there a lead in?
Does a chorus follow the verse or is there a device such as middle 8, bridge, pre chorus etc...is there another device being used that is to verse chorus?
When does the solo, or instrument break happen and for how long?
How do all these parts fit together, are their bar lengths the same, is there a pattern that appears.
How does the song finish, is there an outro or three being used to set up finishing the song?

There is more to it than listed above, the idea is to work out your own method and apply it to your songs.
So what you get is a consistent methodology to apply to in-consistant situations.
The process of learning becomes the same, looking for the same components and working out where they are produces an arrangement you can learn.

So when learning a song, take pen and paper and listen to it, no instrument needed, and write out the bars involved as you listen to it.
The process of the repeated listening to small parts as you write them down is reinforced learning of what is involved, by using your mental process to sort out the arrangement means you can recall what you write easier, in my case i can see a mental picture of the page i am playing, or the lyrics i am singing.

Writing out what you want to play in this way gives you the arrangement by bars, add the chords, or notes being used, once you have the bar arrangement, and you have a written learned arrangement. Notes or chords can be added once you learn the bar arrangement, you just add them at the appropriate places....so again you are going through the song in a deeper way than just remembering it, you are learning it.

The simple way to highlight this is that we all know the alphabet, so what letter comes after 'L'?

Now can you just recall it, or do you have to recite it?

If you can say it you have learned it, if you have to recite you have memorised it, but the point is you can recall the info, but one is more immediate,and since our memories can play tricks on us, such as forgetting things, then learning it is better than remembering it.
Since music flows then immediate recall is needed, there is not time to recite..we need recall, and ignored to have good recall we need to learn, not memorise.
 
Bottom line - I don't love learning songs where I have to count everything, memorize sequences, and pay close attention to what I'm doing.

I like to feel music and get lost in it. That's all that this is all about.
Good point Joe. As bass players, our part is very central in most music, and it's disorienting when we're not.

Bass was the fourth instrument I learned. All the others were ensemble instruments: lots of written parts, sightreading, counting rests, harmonising, no improvising, etc.

I've done so much of that it's second nature to me. Rock is pretty much the other end of the spectrum, so I'm not surprised you're feeling a little uncomfortable. No shortcuts sorry.

I goofed up INXS's Need You Tonight first time I played it. Got right into the song but took the wrong vocal cue and nearly threw the others off. Since then it's purely bar-counting and has worked out fine.
 
I wouldn't rely on counting anything for this song, as it is all over the place. And depending on the vocalist they may or may not sing every line in the same place each night.

My notes for this song would be simple--- Play your eighth note bass part (consisting of two different notes total) whenever the horn part plays (I guess your band has a keyboard doing the horns?) Heck I think the horn part just has the bass programmed in, so when they recorded it there was NO bassist.

For the rest of the song other than the "bridge" just STOP playing anytime Beyonce starts doing her dumb uh-oh, uh-oh parts, rap parts or whatever else. Throw in some completely random slap noises if you feel inclined every now and then like her live bassist does.

Honestly as long as you play along to that horn part the rest of this over-produced fake motown wannabe song just doesn't matter, nor will anyone care.

all you have to do is watch when the keyboard player starts playing that horn part, that's your cue... (or if you have horns, watch for when they play). IGNORE the "vocalizing"
 
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Sometimes I've had occasions when I had to learn too many songs in an extremly too short a time. There wouldn't be enough time to write charts, so I"d just hunker down and play along with the records incessantly as much as I could stand it. Eventually, I got 'em down and had a decent picture in my head for them. But it wasn't easy.
 
I don't know if I would trust myself to be able to purely count my way through this without thinking about squirrels or something.

I would probably write it out something like this:

A3x (You ready?), B2x (Uh oh), A1x, B4x (Verse..understand/no one else can), A4x (Chorus), B6x (Uh oh - Verse..understand/no one else can), A5x .. etc.
...At least until I'd played it for a few gigs.

I see you've already decided to cheat sheet it. After you play this Friday, I'd be interested to hear how it felt to you. Good luck, I'm sure you'll kill it!
 
And to lighten things up a bit :). That other song that seems like math TO ME... whoever the first singer is in this, is one of my new favorite female singers. Not my kind of music, again, but I LOVE the way she sings. Had to watch some live vids of her to confirm it. It's confirmed. She's freaking awesome!

Now you've gone and sent me over the edge. Never heard of her, but she's pretty entertaining.

Seriously, I get your problem. I can read, but hate to do it during performance for all the reasons you and others have already written. The only way I've been ever able to deal with your problem is to chart out the song and practice it over and over until I memorize it. I find the charting to help immensely with the memorization and visualization of the song while I play, even if I'm not referring to it. It's hardest with songs like this one since there's little variation, but this is the only way I know how to do it. I've noticed that people who like this particular music will learn every lyric. That only works for me with songs I like to listen to. Good luck, hopefully they're not all like this. Another trick is to record your band playing the song. Sometimes other members are leaving cues that you're not catching when first performing it.
 
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I think some musicians get in a mindset of having to learn a song in xx:xx time frame and if they go over they're spending too much time.

I'll say this as objectively as possible, because you have only 3 options.

Learn it faithfully: Just spend the time, analyze the song, and put in the effort. Set aside preconceived notions and get it done.

Use a physical reference: If you aren't spending the time to learn the song backwards and forwards, use a chart or reference page. Not ideal, but the only "have your cake and eat it to" option is #1

Create a pattern: Least accurate way, but who really knows that bassline? You could sit Jay-Z, Beyonce, and every writer, engineer, and producer of that song/album down and I bet they couldn't tell you exactly how it goes because it was a cut/paste job.