Just curious. Aside from my tuner pedal I use no pedals. I play the 6 string as well and was once a pedal junky. I divorced myself of the pedals and learned to play a Telecaster straight up into a clean amp (Fender blackface). It was a huge learning opportunity and became more accurate by using only the volume and tone controls on the guitar and all that's available on the amp. I was actually quite surprised on what I was missing, both in my technique (or lack there of) and available tones with just my guitar and amp alone. So naturally moving on to playing bass I found no need for pedals. Am I right or just stubborn. Is there some pedals I should look into? Incidentally, my favorite pedal for guitar was a compressor of all things.
Given you have spent time on your technique and get a good feeling from that, I'd look into pedals that respond to playing technique, or force you to use a certain technique to get good sound out of. An analog octaver requiers specific technique to get it to sound good. An envelope filter is very sensitive to playing dynamics. A gated reverb or delay requires you to stop playing to make it do its thang, where a spring reverb loves a hard hit now and again. I'd start with one of those three areas so you can build on the work you have already done.
Budget is your only factor especially if you want pedals that do a good job a preserving your instrument cable amp tone. (Comps are great too, but you are familiar with what they do, so I left them out.)