I'd be more concerned with temperature shifts during transport, given your location and the time of year! Just bring along a cooler to place the bagged fish in.
Shipped fish, historically, were plastic-bagged with pure oxygen, a good amount of water, and then shipped in styfoam coolers or boxes. Chemicals may be used to calm the fish, reduce stress, or enhance oxygen uptake. They are still often shipped this way. Now-a-days though, many fish ship in special bags that are gas-permeable, and allow oxygen and CO2 to penetrate. These special bags (Kordon brand being one of the popular brands) allow oxygen to diffuse (move) into the bag and CO2 to leave the bag. This allows a smaller volume of water to be used, reducing shipping weights, and keeps the critical gases in the water in good shape. These are the bags many hobbyists use to ship fish. Depending on the fish and the size of the fish, they can survive a week in a Kordon bag, no problems!
The answer to how long can a fish make it in a normal fish-store bag? It depends on the fish size (bigger is not good in this case), the amount of water in the bag (more is better), and the type of fish (fish from low-oxygen environments like catfish are usually more tolerant, a large active red-tailed shark or other very active fish less so).
As mentioned, two hours shouldn't be an issue, but watch the temperature!