How long do I need to drill with my current unit and MOS before I can switch to 11b?

Ahh... Adulting.... Where you have to honor the commitments you've agreed to.
As they've pointed out, your commander is not required to allow you to switch, but you are required to honor your commitment. There is no set time (that I'm aware of) and it's usually driven by local policy.
There are a few ways, all at the commander's discretion. You can move and request a transfer, request to transfer to an Infantry unit, or request to be released to the Active Duty. You're only going to work at your unit 2 days a month, so it's hard to imagine that your lifestyle will be significantly altered by moving to 11B for those 2 days a month. If you don't feel challenged where you are at, I suggest going active and joining the Airborne Infantry and trying out for RASP to become an Airborne Ranger.
Shoot for the moon and if you miss, you'll hit the stars.

In 1974 my CO said it best in the 82nd ABN, "No matter what you do in the Army, Remember, your primary job is infantry". And, don't tell me if you are a cook, supply or you repair M-16's in the arms room, if the enemy is about to overrun your position, "You Become Infantry", and pick up a rifle and fight for your life.

If you’re in the NG need to find an infantry unit that will take you, give you a paragraph line number as as payroll number let both Readiness NCOs know what your plans are and do a 4187 requesting to reclass to 11B. I think you have to be at your current unit for a year.