As said previously, tube vs solid state isn't that much of a factor, in my opinion, especially on bass (relatively low gain compared to guitar, full on distortion would be a crunch on most guitar amps). The fact that tubes produces a better distortion is also an assertion that needs to be qualified. There are people who maintain that you can have perfectly adequate distortion, with a nice "tubey" feel, without using a single tube. Also, even on guitar, more than the overdriven device (tube, solid state, whatever) it is the filtering that makes most of the character, with the device mostly affecting the touch sensitivity, and even then... I designed and simulated my own bass/guitar amplifier, which I will get round to building eventually, one day... using a combination of opamps, FETs and different LEDs shunted to ground with a series resistor to provide asymmetrical soft clipping - you can even use bipolar transistors in a certain configuration to achieve an even more dynamic soft clipping, but if the sim is correct I still get a very progressive transition to distortion, so the idea that solid state devices cause abrupt distortion needs to be qualified as well.
In other words, it all depends on the design (how much feedback is employed in each amplifying stage, is it geared towards maximum quasi-linearity or for gradual breakup? Is it intended to be played into overdrive or is overdrive just slamming the amp very hard?). The Orange Terror Bass for example was a hybrid amp that was basically an overdrive machine, with breakup as early as 10 o'clock on the gain pot - by the way, I never liked it, I've always found it dark and muddy - while the Mesa Buster, 200W all-tube, is comparatively hi-fi.
Anyway, why don't you consider a Marshall JCM bass amp? Or a VBA400? They are actually very nice amps in my opinion.