BP's reply got it pretty perfectly. Sit him down, explain things to him as BP laid them out, them come up with a plan together to make this work for both of you.
It may be that you two develop a hard set of rules "Always give me 3 days notice and 1 day to say "no" (if I can explain why that day is a problem) before scheduling any dates, no more than one date per week with her, overnights every two weeks tops, you and I must have one date out of the house per week minimum, etc etc" OR you can create a general set of guidelines "Communicate with me if at all possible before making any firm plans, try to make sure you're spending as least as much time with me and giving me at least as much focused energy as her, each of us will do our best to clearly communicate if we're having any problems as soon as possible, etc etc."
I would recommend leaning towards the latter over the former, but the occasional rule, if he's really having trouble shaking the haze of NRE, might be a good idea.
The major players. Me, 30ish bi female. Gia, girlfriend of 4+ years. Clay, boyfriend/dom. Davis, ex/friend/"it's complicated." Eddie, roommate & fwb.
The supporting cast. Eric, Gia's husband. Bee, Gia and Eric's toddler. Dexter, Gia's lover. Helen, Eric's lover. Izzy and Nikki, Clay's partners. Liam, Eddie's husband.