It doesn't happen under $100, sorry. It's not quite this simple, but basically for speaker design—low cost, has bass, plays a reasonable volume: choose two (and nobody chooses to make speakers that play really soft only, let's be real). The laws of physics and business realities, in terms of what is feasible to physically produce and sell for $100 and under and make a profit, mean that your selection criteria rules out everything in existence. Other than possibly some steal of a deal you find used.
It's a little more possible if you skimp on a 2.1 set, making the satellites really dinky and having the compromise of having those dinky satellites and lower midrange coming out of the super-budget subwoofer. But still, not a great look.
You could also technically Frankenstein a setup with real budget pieces and judicious EQ (to bring everything but the bass way down, potentially also to ameliorate some other problems somewhat) and tune that to sound decent, maybe. Though at the cost of volume.
So, unfortunately, the question is what part you're willing to compromise on. (e.g. price, bass, etc.)
Some kind of reasonable-ish compromise, keeping the price, may be just a Dayton Audio B652-based setup. It really depends on what you need.