first calm down and dont be terrified. (probably easier to say than do.LOL) find the key of the song. either u can ask the organist/keyboardist or at the end of the last verse where the song feels complete find the note that best resonates there, that would be the 1 (root or key of the song). try singing along and then hold that note and match it on the bass.
the first verse revolves around the 1 as well but if ur organist/keyboardist is busy it may be harder to find that note because of his movements.
Each part verse revolves around a particular chord. so the first "cant no body do me like jesus" would revolve around the I chord. staying with the tempo of the song u could just bounce on the root and the fifth and when it changes to the second "cant nobody do me like the lord" just chromatic walk up to the next chord root which is the IV (4).
if the song is in the key of D the first "cant nobody..." would center around a D chord so you can just alternate hitting D and A (or what i do is D,A,D,A,C,Db,D,A,D [1,5,1,5,b7,7 pattern]) then for the second "cant nobody..." the song would go to Gb so right before u get ready to play G walk up to it chromatically by playing E,F,F#,then the G. (u can add more notes or take a way depending on ur timing) then alternate between the G and D (root and fifth) on the end of the second part "do me like the lord" you can chromatically walk down to the 2 and to do a 2-5-1 (so you bounce on the with that IV chord and as soon as the say nobody walk down from the 4 (G,F#,F) then go right into the 2-5-1 (E,A,D). Then the last "cant nobody..." does the same as the first one and centers around the I, but as soon as they say "nobody" walk down from the 1 to the 6 (D,Db,C,B) and on "hes my friend" is a 3-6-2-5-1 so its (he's) F#,B (my) E,A (friend) D. then i chromatically walk up from the 3 the 5, the from the 6 to the 1 (the shout walk) and when i hit the 1 the song is ready to start over.
For the vamp on all those you can just do the basic "shout walk" and vary that.
most of those songs have a similar feel but 1 or 2 parts of the progression may be different so you gotta hear it. i understand with the hymn book thing, but if they do like at my church, because all the songs have the same beat, they may run them together as a medley going right in to the next one, and at that point lookin in the him book aint worth a hill o' beans. Especially if its a song that aint in there (all of them aint in there) and we never know ahead of time. a hint: always know the words to the songs so you know when it changes. if the song changes and you not sure what to play, turn your bass down and sing along catching the changes matchin it on ur bass, and when ur confident of the changes turn ur volume back up. thats the best way to do it because then you'll be better able to play with anybody. my organist can at most tell you what key he's playin in and thats it. Chords?!?! forget it.
the thing is its hard finding a recording of these songs to hear what a bass player is doing. i learned off of Fred Hammonds' "Somethin' 'Bout Love" album, he had 2 interlude tracks both about 30 seconds, but that helped a lot. One was "God is a Good God" and the other was "Im a soldier in the army of the lord". If you can get to listen to these you'll hear exactly what im talkin about. Even though they were both only 30-second tracks, for my playing they were priceless.