I imagine Bateson's ears pricked up when he heard the Enterprise-E had traveled back into the past following the Borg attack. "A way back to my own time? Tell me more!" Remember, the Bozeman was right there at the scene.
Whether Starfleet would let him do it is another question, of course.
No kidding. There really isn't any difference being shot forward in time like Enterprise-C or getting stuck in a time loop and coming out of it in the future. Imagine what TNG could be like if the Bozeman went back to when it left. Who knows, they might've done something to cause Q to meet up with the E-D at a later time thus allowing more time for the Federation to get stronger before encountering the Borg...
I had been under the impression that although the Bozeman had been at that battle, the ship had already been destroyed. Granted, Bateman survived to appear in the Destiny books, but I thought Bozeman was wiped.