There's lots of good news when it comes to bass amps, but a little bad new as well. The bad news; to amplify bass frequencies enough to compete with an electric guitar takes a lot of power. I've used 15 watt guitar amps at gigs but I would want at least 100 watts for a bass amp that was going to be gigged. Ditto for the speaker size. There are some small speakers that sound great, but IMO, basses reallly sound best with a good sized cabinet. Good-sized usually means fairly heavy.
Now for the good news. Bass amps don't have to cost an arm and a leg. A fairly straightforward solid-state amp can sound pretty good for bass. seperate heads and cabinets are fairly common in the bass world. For inexpensive but durable and good sounding cabinets I suggest looking into Avatar speaker cabinets. I have a 112 and it's absolutely great. I won't recommend any particular heads except to say that you tend to get what you pay for.
Another approach is a small combo bass amp. Fender has the TV Bassman series with tube pre-amps. IMO the 1x12 model would be pretty good for most small gigs.
Talk to me - I may have an amp for you! Will I be seeing you at the Big House this afternoon?
Generally, for wattage, a bass amp needs to have 4x the wattage of the guitarist's amp to come over the top properly.
You can probably get away with one amp for both eletric and upright bass. I use the same amp for both upright and electric, although I use different speaker cabinets for various size gigs. My amp is a 300 watt Clarus Acoustic Image, which is popular amongst upright bassists (although not necessarily on the rockabilly circuit). I like it because it sounds good when I use a bow on the upright. It also sounds great with my electric Fenders
My cabinet for small gigs is an Ampeg Portabass 1x12. I can use this for restaurant gigs, jazz gigs, and small halls. If I'm playing large outdoor type gigs, I add an Avatar 212 Neo cabinet. I've never used the Avatar with the upright.
Prior to getting the Clarus/Ampeg rig, I used an Ampeg B2 combo with a 1x15 speaker, which is about 350 watts, IIRC. That amp would work great for rockabilly upright and electric. It didn't sound that great with a bow, for me, though.
That Bose can be used as a bass amp with no problem, you also have the bass speaker to help you. Otherise that Genz-Benz Shuttle that RJ uses is a good amp. The combo, amp and cabnet sells for $699.00. But there is no reson to buy a base amp when the Bose will handle anything you will need.
I did 88 between yesterday and today. Rain coming, so no riding tomorrow or Sunday.
Sides that my wife has homework so I'll have the kids all day tomorrow, and I'm going to see KISS Saturday night. Sunday will be recovery.
I don't get to court as often these days. I am doing more estate planning and transactional work.
Do you play classical? What music is best with a bow?