Generally I acknowledge that that friend now has other priorities, and I wish them well and go about my own life. Depending on the friend, I'll likely remain available for whatever interactions they want, but my life doesn't revolve around them any more than theirs revolves around mine. A good friendship doesn't need to be coddled every day in order to endure, and I certainly don't want to get in the way of my friend possibly finding a good long-term romantic relationship. That said, I think it's even more important for me to back off in the early stages of dating since most of my close friends are male, and new girlfriends often seem to feel threatened by the lifelong female friend of their new boyfriend, so I give them time to get to know each other without that potential insecurity.
These friends had to go through the same adjustment when I dated and then married the man of my life, and even moreso when I had kids -- those who made the adjustment and were just happy that I was happy are still in my life, those who acted like petulant children because they were no longer the center of attention are not. I don't have the time for anyone who will try to make me feel guilty for not spending more time with them when I have a family and business to attend to, and I would expect them not to have time for me if I behaved in the same way -- I'm not entitled to be a priority in their life.