Two very different instruments that have two very different amplification requirements.
Guitar amplifiers and speakers in general contribute much more to the overall
sound of the instrument than the majority of bass amps. A lot of that sound is due to
technical short-comings of the components originally used - valve distortion and speaker
with a very uneven frequency response. That means if you want THAT guitar sound you are
still tied in to design and technology from 50-60 years ago while bass amplification has
moved on a lot and these days has far more in common with good PA design. BTW the size of
the drivers in modern bass amplification far less important than the overall design of the
cab that they are housed in.
Bass guitars also need A LOT more power in order
to be heard. For gigging, the general rule of thumb is 100W plus 3 times the combined
power of the rest of the band's back line.
Also unless the bass sound you want
is strictly old-school 50s and 60s mainly muddy and dirty the Fender Bassman is not really
suitable as a bass amp these days (coupled with the fact that they are woefully
underpowered by modern standards) which is why the majority of them you see are being used
by guitarists only.
You could experiment with running the guitar through a Pod
or some other amp sim device into a bass amp with plenty of clean headroom, but ultimately
I think you'll find yourself disappointed with the sound of one if not both instruments
when you are compromising this way. Plus you are likely to have massive volume
discrepancies between the two.
What sort of music are you playing? That will
have a lot to do with what sort of amps you should be using - especially on the bass side.