I'm not the most qualified here for your query, but it's so sad nobody answers! Hope more people will jump in.
Baking soda is a candidate, yes. You will get a faster reaction using a more convincing acid than vinegar, which doesn't mean corrosive. Tartaric acid (among others) is civilized and reacts promptly
http://en.wikipedia.org/wiki/Tartaric_acidbeware baking soda produces much gas, so use the right amount of soda or acid.
Either the right amount exactly, or have a vent that opens when the desired volume or overpressure is obtained, or inflate a very strong container (less secure).
Baking soda uses to produce a foam, as the bubbles appear within the mixed liquids.
Among
foams, I know polyurethane, easily available. I feel it less suitable, as it is viscous and needs to be mixed, or expands from a bottle. Harder to remove thereafter.
Could you inflate your object with gas from a small bottle? CO
2 exists as sparkler for drinking water. May be loud.