Hi Georganne - there are lots of good we resources - some with more "theory" behind them than others.  Here's one - it's intended for guitar - BUT - it calls out the theory and talks/shows the tonal separation ( like whole or half steps etc ) in the key and mode chosen.  Talking about modes, major or minor pentatonic tend to work very well for simple improv to many tunes...  

Check out https://www.guitartonemaster.com/node/8 for some backing tracks to improve to - also just google backing tracks - there's a lot of stuff of limited use, but you can find some gems....

Also, for a REAL good handle on the theory - https://www.basicmusictheory.com/ is definitely worth a visit - although I'm pretty sure you'll know, or have learned/become aware of most of it...

Good luck with your improv quest !

[ Just to add - one of the things I do find sort of difficult is when a tune is new to me and I try to play along, I, possibly similar to what you're describing, get "stuck" with the melody line.  I can't break away from it until I reach the point where I no longer have to specifically focus on, or think about what notes I'm playing.  Once it becomes "automatic" (which can take MANY MANY play throughs over a period of time), suddenly the door opens - I'm no longer focusing on a note-by-note progression, but the feel of the tune as a whole - and yes - I'm doing simple variations, improvs, throw-in little riffs and so on that make it my own so to speak.  I have every confidence - you'll get there ! ]