Bass speakers move considerably more air than guitar speakers and, as a result, need a lot more power. If you underpower your speakers there are all sorts of negative outcomes, both from potential damage to the fact that you'll have to crank you little amp up so loud it clips like crazy and you have terrible tone no matter how hot those tubes get.
You don't want tube power, you want a tube preamp, which will give you the overdriven sound you want without relying on tubes to actually power your speakers. There are tons of options here, like preamp pedals that either digitally reproduce the sound of tube overdrive (for example, Darkglass) to units that actually have real tubes in them (Ex: EBS Valve Drive). You don't need a pedal for this, either. A preamp like the old BBE BMAX can give you a ton of tube warmth even when driving your speakers with solid state power.
If I were in your shoes I would do some serious homework before spending money on an amplifier, unless you have a lot of extra cash to spend replacing the stuff you buy that doesn't work.