1994 virago idles fine won,t accelerate only runs with choke on

is the air filter good, not restricting air flow, is the choke turning off ok

sounds like a pilot jet problem. Pilot jet runs first 1/4 of throttle opening, main jet the other 3/4. Take out pilot jet (usually the smaller one next to the bigger main jet) and leave it in a cup of neat petrol overnight. By morning it should be ok.

There is possibly some dirt blocking the main jet supply or the float level has somehow dropped and the engine needs the extra suction to draw enough fuel in to keep running and it is supplementing this extra supply through the idle jets.

The problems with a plunger style choke happen when the rubber on the bottom becomes deformed and does not seal or the spring does not push the plunger down hard enough, or the cap breaks so the plunger is not pushed down hard enough. If you put your finger over the hole and the bike runs properly your bike is running on choke. You have to block the hole deep inside the carb to shut off the choke. I assume the original problem was that the bike would not idle .If this is the case, take the carb apart remove the slow jet and clean the jet and the carb body out so fuel will flow at idle. This should fix your no idle problem.