If you want to do some kind of research work over the summer, yes, absolutely you should be talking to your professors. The formal REU programs are one option, but they're not the only one. Talk to your professors and ask if they know anyone who is looking for a summer student (and the earlier you do this, the better).
Many schools have a thesis-option for senior students. If you're planning on doing this next year, one option might be to approach some of the professors who regularly supervise undergraduate students for these projects and ask if you can start early. They may not have funding to support you, but it's something that you can work on in your spare time over the summer.
The other thing to keep in mind is that if a research position doesn't work out, don't worry too much about it. It's great to grab these opportunities, but if they're not available, you can pivot and focus on something else - start your own business, or try to find the highest paying position you can to earn money so you don't have to work during the school year. As you said, the bills need to be paid.