You will be able to get a Compass Card at the airport, either before or after you claim your baggage.
From the MTS web site:
Ticket Vending Machines for MTS services are located near the Information Centers of both Terminals 1 and 2, as well as at the Middletown and Santa Fe Depot stations. Ticket Vending Machines sell Compass Cards with one day passes, multiple-day passes, and monthly passes. You may also reload your existing Compass Card. The machines accept cash (and give change up to $15) and credit cards.
In Terminal 1 the information center is across from baggage carousel 2. In Terminal 2 the information center is between baggage carousels 3 and 4.
If you exit baggage claim in Terminal 1, the bus stop will be directly ahead of you. If you exit baggage claim in Terminal 2, turn left when coming out the doors to reach the bus stop.