My 1991 Chevy Silverado starts up ok, but has a rough idle until it warms up. Once it is warm, it runs good unless you try to accelerate real fast. It then bogs and backfires

It may be the idle air control valve is all plugged up. It is on the passenger side of the TBI, square plug. Should probably take the IAC valve out, then take the TBI off and clean it up good along with the port for the IAC valve. Then you can check the base gasket at the same time as they will go bad. Once this is done then see what it does. It may be that the fuel regulator in the TBI is needing to be replaced. Fuel pressure should be 9 to 13 lbs. Check with a gauge and rev the engine up to see if it holds fuel pressure within the range.

check your fuel filter? when was the last time you had it changed? also they can wear out a fuel pump, so beware if it was the fuel filter, then most likely it will not be long before your fuel pump goes (only because it strains and wears pump down)