[jonnathanson]

"Time dilation occurs at speeds far less than the speed of light. For instance GPS satellites and jet planes experience measurable time dilation."

Sure, but I think (?) the original question was asking about time dilation in the massive sense: i.e., you go on a round trip to some distant point in space and return, and it's only been a few days for you, but a few hundred or thousand years have passed on Earth. That sort of time dilation.

That sort won't occur with an Alcubierre ship. It's my understanding that the ship isn't actually moving at all inside the bubble -- or, if it is, it's moving extremely slowly.