Is it too late to plant begonia bulbs? I live in the DC area (my zone is 6 if that helps)?

No, but they will flower a lot later than you might expect. I live in zone 6 near Lake Ontario and to get good foliage and flowers before late summer, we start bulbs mid March to early April indoors. May keep in dark until leaves start to develop. Don't place out until danger of frost is past, (used to be Memorial day, but earlier lately. You can always bring inside if cold is predicted) I started mine late last year but planted with low annuals to make up for slow growth. If you have extra cash, you can buy already started plants at a nursery. Gorgeous flowers and well worth the extra effort.