Swing --- First you got to do a lot of listening to hear Swing.
There is Texas Swing which will have a fiddle in there somewhere.
Texas swing is danceable.
Picture 1930's big band sound done by good ole boys.
Grab a chord and pound out roots till something else is needed. You probably will not go beyond root fives.
Then there is gospel swing.....
video gospel swing - Bing video Again roots till there is room for something more.
Then there is black gospel
Aretha Franklin Gospel - Bing video I'd lay out on this one. There are some songs that it is best we lay out and this is one of them IMO. Now how much of each your band get's into I must leave to you. Be a sponge and soak it up.
It's the rhythm, more than actual notes. Start with roots and if there is room for more notes my ole standby is insert a 5 still need more bring in an 8. Still need more.... you are moving into jazz improvisational gospel. These cats are great musicians and steeped in gospel since they were at Mother's knee.
Improvisational gospel -- as the minister gets to the end of the message the keyboard moves back to the front and starts improvising a soft melody under the message being given. He is joined later by the rhythm section and they jam together augmenting the message as it unfolds. Gotta witness this.......
Gotta mention Shout Gospel and there is a specific bass line technique for this style;
shout gospel - Bing video
Back to the original question. Get the chord chart, don't argue with what has been written, pound out roots to the beat, listen for where there is a void that needs more. When you find that void, fill it.