Most likely causes:
Not cutting the curds small enough - should be the size of a rice grain. Use a whisk.
Under cooking - could be temperature or time, or both.
Inadequate stirring. Stirring promotes syneresis (expelling whey from the curds). Clumping traps whey.
Inadequate drainage prior to hooping. Don't rush.
Draining longer also gives the bacteria time to develop more acid. Lower pH means drier and crumblier.
Pressing too hard initially. Asiago is a thermo cheese, so it doesn't take much for the curds to fuse.
Press longer not harder.
If you used Lipase, you might have used too much. Lipase is an enzyme so a little goes a long way.
Aging longer will often eliminate bitter notes.
Asiago is typically produced in 3 variations - young, medium, and aged. If you want a softer, milder Asiago, try washing the curds a little.
I have some 2-1/2 year old Asiago right now that is to die for.