The Roland cube is a great amp but (my opinion) it'll leave you feeling unhappy with the bass. I don't think you'll struggle to get an amp that sounds good with both the uke you already have and a uke bass but you're going to need to really focus on getting a larger speaker and enough watts for the bass, regardless of the tone or other features. It's easy to amplify a high pitched instrument without a lot of power, but bass frequencies really need a lot of air movement.
I would echo the advice above - avoid amps that focus on modeling since most of them are targeted at things you're not looking for (i.e. copying a specific electric guitar tone, making an electric guitar sound acoustic or vice-versa, etc).
There are a lot of good acoustic guitar combos out there, but the ones in your price range almost universally have small speakers and less power, which (not to sound like a broken record here!) is why I'd stick with a bass amp for your two proposed uses. It'll be much easier to find a cheap bass amp that the uke will sound good through, than to find a cheap acoustic guitar amp that the bass will sound good through. And u basses have such an amazing deep thumpy tone, it would be a shame to neuter it by playing through a tiny speaker.
I like the Fender Rumble amps among the cheaper bass combos. One benefit of them is that they sell a billion of them so they're all over the place (makes it easy to try one out locally, and also easy to find one used if you're inclined). Ampeg makes good small combos too, and they're widely available, but they sound "like an Ampeg" - some people love that and some hate it (I'd guess you'll hate it based on your needs - people who want the Ampeg tone generally know that ahead of time). If you're willing to stretch your budget a bit or look for something used, I like the Warwick combos (BC 20 will be maybe $125 used) or the smaller Hartke combos. Hartke bass combos use aluminum speakers which give them a pretty bright tone, should work well for the uke.
As always the best thing to do is get out and play as many amps as you can find...