I use a nose clip and have no trouble breathing. I can even breathe out through the nose, although I'm sure it would be easier without the clip. It is of course also possible to breathe out through the mouth only. I think the secret is to relax and breathe out slowly but steadily.
As a lifetime breaststroker breathing out under water has never been a problem, but as a recent convert to freestyle, thanks to TI, I still struggle to breathe on the 'wrong' side. I think the answer is lots of underswitch and one-arm freestyle, both of which have other benefits as well, I believe.
I would suggest lots of 25m and 50m repeats concentrating on relaxed breathing, and of course some of the head bobbing practices mentioned elsewhere would do no harm.