Bass needs a lot more power because we don't hear lower frequencies as well as guitar. (Given the same general compliment of speakers.)
There are lower power guitar amps just like bass, but power ranges for bass get a lot higher just because guitars don't need as much to be heard.
Usually with a bass amp, if you do larger speakers or more speakers or both, that is a much more efficient way of getting louder. Doing it with mostly just power isn't gonna cut it very well.
I say, also as a blind guess, the bare minimum is going to be 300 watts and a couple of fifteens. But there is so much variation in equipment that we can only give generic recommendations.
What ever combination of amp and head, or combo, you get, be sure you can add a second matching cabinet.
That way you can get a lot louder by adding the cab instead of having to buy more of everything again.
All of this assumes you have no P.A. support for instruments. If you do, that can change the whole formula.