................ So, what am I missing here? Do people just solo in some basic scale/mode regardless of the harmony? Or is it a mix of both? How do I go about incorporating harmonic elements into a solo? Or should I just shut up and play the Eb blues scale and be done with it? Thanks!
How do you improvise? With out some theory background, good luck. OK dirt simple:
Music sounds good when we use the notes found in one key. That alone makes it doable, still hard, but doable. So..... Stay in key.
No it is not necessary to know everything that could work. What could work comes later. How much later? Depends on how much time you spend building a dirt simple understanding of how music thinks.
The music I play has an established tune. Start there. Then improvise your interpretation of that tune. Augment what has already been written.
If you can not play the tune, good luck with improvising anything that sounds anything like the tune. That leaves you with scales or chord tone over and over till it's time to give the lead back. That's one way, but, IMO you gotta get the tune in there somewhere.
Sing the tune and see what your fingers can do with that information. Again a little theory study will go a long way.....
...Theory works on any instrument - here is a book I found helpful; JoyOfImprov, book 1. It's a Hal Leonard book by Dave Frank & John Amaral. It's not a bass book, it's a theory book for any instrument. What is in it you can use with any instrument. Because of that bass tabs are not shown, however, standard notation and scale degree numbers are shown.
As I think in scale degree numbers anyway I found this book to have value. Here is an example:
Over a Cmaj7 chord you could use the following scale degrees of the C major scale: 137, 1357, 3561, 3571,..... 369, 3569, 5613, ...... 5713, 7135, or 7935. When you understand why that works, you can take it over any chord. Major's have the 3 & 7, minors have the b3 & b7. The following Cm7 chord example implies playing the notes of the C natural minor scale as your base, i.e. 1-2
b3-4-5-
b6-
b7. So using the natural minor box pattern the following does work.
Cm7 chord is shown as: 137, 13
117, 1357..... 1457, 3571, 3679,,,,,5713, 7135, 7935. Book # 2 goes into more detail.
Have fun.