I store 2 days worth of firewood in a rack near the wood stove which has been fine for the few years that I've been burning wood for heat.
Never had a problem with bugs or anything but I mostly keep all my firewood on the covered porch in a firewood rack and then bring in one days load of firewood every time I go outside and come back in that way I always have firewood next to the stove to burn without always having to walk out to the porch to get more firewood.