I have driven from Washington DC to Williamsburg on quite a few occassions (live in DC, parents live in Williambsurg)

I think generally a rental car would be best but partially depends on what time you are arriving, what your preference for driving vs. train, how much time you have and what (if anything) you want to to while in Williamsburg.

Its a relatively slow / inneficient train ride because it goes to Richmond and goes very slow through the Richmond area. I have taken it from Washington DC on occassion. Its probably 4.5 - 5.0 hours from BWI to Williamsburg.

However, if you won't be leaving your hotel and really don't feel like driving and don't mind sitting on the train for a long time it could be a consideration.

Further, if you happened to be arriving on, for example, a Friday afternoon, the drive from BWI to Williamsburg would be rather painful.

I am sure your tickets are already bought, but flying into Richmond or Norfolk, VA (or even Dulles) would be much closer but i suspect more expensive which is probably why you are flying into BWI.