DCA is a small airport - that's in your favor. American uses gates B and C. What airline to you have to connect to?

Re-reading - is your flight to Bradley on American too? If so, I would think no problem. The two concourses, B and C, are not far apart - easy walking distances. Only problem would be if your bags are not checked all the way through to Bradley.

If it's a real small jet, they might fly out of gate 35X (I think that's the number). That's actually a bus that takes you out on the tarmac. This will be replaced sometime in 2021 with a new terminal beyond the existing terminal C - the new terminal is not open yet (but appears to be substantially complete).