The Maryland Transportation Authority announced the best times to travel across the Chesapeake Bay Bridge as you make your way home from your Memorial Day travels. Eastbound: Monday, May 26th – before 10 a.m. and after 5 p.m or Tuesday, May 27th – before 7 a.m. and after 7 p.m. Westbound: Monday, May 26th – before 9 a.m. and after 10 p.m.or Tuesday, May 27th – before 6 a.m. and after 6 p.m.