Sounds to me like you are having issues with the chords, runs, etc and not the rhythm? If so, keep in mind that most gospel songs are very simple repeating patterns (chord progressions). The difference is that the bass rarely plays the root. That is why the chords sound so different in that at any particular time you may be playing the 3rd, 6th, flat 5th, flat 6th, etc.
So the progression may be actually only a few different chord intervals, but because the bass it playing many different chord tones it sounds like a lot more. For example, check out Micah Stampley: Worthy to be Praised. The progression is a 6, 2Maj, 1, 2, 5, 1 where the bass does uses a leading tone walking through the 3rds, which ends up being a chromatic tone lead from the 5th to the 3rd of the key. Dissect this some and you will be on your way to understanding gospel.
Also, the runs are mostly pentatonic in nature with an altered note thrown in. I.e. 6, 1, 3, flat 5, 3-2-3, 1, 6.
Hope this helps, good luck.
+1000
Im a straight-ahead jazz bassist, I came out of everything 50s, and 60s. I've studied, transcribed, taught, written books. I can confidently say I know my theory and I know my instrument, but when I got my Gospel gig, I left thinking "what was that!?"
So I think your experience might be the norm if you didn't grow up in the church.
If you have a confident (strong back ground) in another style, i.e. Jazz or Classical you can certainly learn Gospel. But it has to be
learned. Think back to playing all those Abersold play-a-longs. You're gonna have to do that again but transcribe it.
As far as patterns theres some basic stuff you need to get up front:
Learn the basic "runs" and "walk-ups" over turnarounds (cadences)
Get use to the different note placement for 6/8 and 4/4 walk-ups.
Understand the difference between I-IV "runs" and I-V "runs".
Pickup some of the cliche turnarounds for Tags at the end of songs.
Know your harmony not just from the root up but from the 3rd up and the 7th down. The contemporary gospel stuff will use basic harmony built off an alternate bass note; i.e. Db/F (which is still just a triad but in first inversionwith the 3rd in the bass)
Start to recognize the use of pentatonic licks Major (and Minor) for fills within a progression.
Rhythmically, every era has a different feel to the beat. Be true to the the style of the arrangement.
This all relates to the way Jazz players learn the basics;
Ellington or Basie endings, or cliches like
The Theme to end a set, or shout choruses, etc.
The groups listed are great, I'll throw in Byron Cage, Richard Smallwood, Donnie McClurkin, and definitely Rev. James Cleveland.
Good luck, play on!