If you only ever want air to LEAVE* the dry bag (in burp mode) and you unroll the neck to get into it, there are tiny little check-valves in the aquarium aisle of Walmart, Petco and any pet store. Whether you mount it directly into a corner of your dry bag or attach it to a length of vinyl tubing, if you point it to flow OUT, then every manipulation of the bag will make it smaller in volume.

*to reverse the function (fill the bag), you could simply give the check valve a yank to detach it from a length of vinyl tubing. A puff of air by mouth would then quickly pressurize the bag.
A high-flow version is in some skin-diving snorkels and I look for them at Salvation Army. It is also a low-pressure flapper check valve, but 3/4″ to 1″ in diameter so it allows a much higher flow through it. When present, they are located at the low point of the snorkel so that one may more quickly clear the snorkel of sea water. I doubt you need that for the size of dry bag you’re using, but if someone had a bigger set-up. . .