What are the chances of ovulating first month of birth control? I started taking lutera the sunday after my period. I was still bleeding a little.

Some. There is no absolute in birth control with birth control pills. Usually good control at 3 or more months.
Ovulation on OCPs. I generally recommend using a back up method of birth control the first month. After that, if used correctly, your chances of ovulation are less. Perfect use for birth control pills has a 0.3% failure rate, but a typical use failure rate of 8 %. It is normal to have break through bleeding in the first 2-3 cycles of birth control pills. I recommend continuing through the third pack.