I'm going to sound like I'm fawning over you two sods, now, but you're absolutely spot on. Solo bass is an art in and of itself, and it's beyond the realms of what I find enjoying - if that's what I was looking for in the bass, I'd have been required to give in a long time ago. Or start wearing a beard and a high waistband, or something. I'm not sure which.
The bass is there to drive a song along, tying in the melody with the rhythm - which is why it finally all comes together when you're playing with others, and you're sat in the role and holding things together. It's definitely an eye opener, making the leap from playing solo.
As you're sans band, do you have some mates you could jam along with? Failing that, I used to get a lot of inspiration from playing along to favourite records - working out what was being played, and then deciding how I would do it given the chance. Was a useful exercise in understanding the role of the bass and flexing a little creativity.