I would also recommend annotated sheet music for sight reading that tells what string and fingering to use. Depending on the scale or your bass, but most notes will occur 3 times on the fingerboard. It isn't always clear at the start of a section that you should be holding a Barre or that you should be in 10th position instead of 5th.
Last bit, some music you just cannot sight read. This video is of violinists learning a piece over a year or two. They are professional classically trained violinists. The one that actually ends up learning it has perfect pitch (I recommend looking up that video too). I like this video because you get to see their initial playthrough and the final result which is still not perfect.
I have been studying one piece of music for 2 months that I have memorized but is far from perfect. I am not professional by any means. My instructor is about 80 and so has 60 years of classical training and also cannot sight read everything. I only mention this, because people think if you practice enough you can sight read everything. There is just no way.
In the industry when they expect you to sigh read, they probably refer to section musicians. What you are talking about here is how to play as a soloist and they usually do not have charts in front of them. But the orchestra does and the conductor may have some subtle changes that the section musicians must be able to cold sight-read. Soloist are not hired, they are scouted.
Musicals for examples, they will re-imagine certain songs from how it is normally played and you are expected to read the different versions cold. So if you practiced a certain version, you have to unlearn that quickly and play as the director intends to that night and it may be different from one show to another.
If you can do these things on a typical session gig:
You are given your chart. The tune is about 4 pages long. You glance at them. Immediately you know how it is sectioned out. You know the key and you know when the key may change. You will be aware that there are dynamic and temp changes. The tempo is called out. You play and execute and there are bar 67, there is a note that is not part of the key and in the next section you have to play eight note triplets. You do all this without getting lost and with the band. You are also new, do not know everyone's names and have not heard the tune before. You repeat the same process above for 30 more tunes, some you know, some re-arranged. You will not have the time to rehearse in some cases. Also as a bass player, there maybe a couple of tunes, where you have to play a solo but it is written out, not improvised by you. You have to nail that too. That is sight reading. How you get there, many things work for different people. But I think as an adult in late 3o's or 40's, it maybe too late. Not saying you can't play or be a great soloist, but musical directors may not hire you.
And yes, some people who cold sight read so well maybe absolute wrecks when asked to improvise or play with chords or jams.
This is different from being given some sheet music, you learn it, come to a rehearsals and the band probably sounds bad the first time around or have their own way of playing it. Like in Jazz combos.
Meanwhile, the sad reality is, the guy with pro-tools who uses a computer to lay out a whole backing track is thew one who Beyonce hires and even gets a grammy even when they cannot even read. And DJs get the gigs and make people dance.
