Many have a minhag to eat a milchige meal (and milk and honey) on Shavuos. Some eat milchigs at night and fleishigs at the day meal, while others eat milchigs, bentch, and then wash again, and eat fleishigs to be yotze Simchas Yom Tov with meat (Shulchan Aruch w/Mishnah Brurah 494:3).
If one eats milchigs, but not “hard cheese” (which requires one to wait six hours before eating meat), one need not bentch and wash again before eating meat. However, one should wash his/her mouth well and the tablecloth should be changed. (Other poskim require one to bentch.) See Shulchan Aruch w/Mishnah Brurah 494:3, Piskei Tshuvos 494:12.