It's not the acellerator pump, or it would acellerate bad when it's warm as well.

The general running crappy is probably a result of the plugs fouling and misfiring.  The longer drive to the shop probably allowed the plug to clear, and then run okay.

This means you probably have a choke pull off problem.  It often occours from just age, or from someone cleaning the carb with a very stout cleaner that damages the pulloff rubber diaphram.  This usually takes a few days to see the failure take place, and symptoms to occour.   Not saying the caused the pull off failure.  During a complete rebuild it would be removed on disassembly, and not be subject to the cleaners.

That little bit of additional information helps to perhaps narrow it down.  Have them check the pull off.