Bass amplifiers, even more than guitar amps, have crazy variations in wattage. Just a quick search of Sweetwater.com turns up 20W bass amps, 2,000W bass amps, and everything in between! But do you really need a 2,000W amp? The answer depends on your use.
In general, bass amps need higher wattages than guitar amps because bass amps require more headroom to push a strong, clean low-end signal to cabinets filled with large speakers for projecting low end. If you’re looking for a home practice amp and won’t be playing with a drummer, you may be fine with a great sounding lower-wattage bass amp.
If you’re playing with a drummer, in a rehearsal space, and maybe playing shows, then you’ll likely need a higher-wattage amp. A rough, general rule some players use is to make sure your bass can keep up with the guitar, you want your bass amp to put out anywhere from two to four times more wattage than the guitar amp. (There are many factors that can affect this, not least of which are the bass amp speaker configuration, the efficiency of the speaker(s), your desired tone, the guitarist’s tone, and more. Still, it is a place to start.) So if you’re playing with a guitarist who has a 50W amp, that would equate to a 100W to 200W bass amp. If your band has multiple guitarists, guitarists who play down in the bass range with an 8-string or other extended range guitar, a keyboard player who uses synth bass or bass heavy patches, or if your band places at very high levels, you might want even more.