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4.5 hour ride from Baltimore
3.5 hour ride from downtown Philadelphia

you could also take Amtrak to Wilmongton, DE and transfer to DART #305 bus
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I have heard Carolina Bus company has a route from Baltimore to Rehoboth, but Greyhound does also> There's a chance Carolina bus company may have been bought out by another, but here's the phone number I have for them. Maryland Mass Transit Authority has a bus that runs to Annapolis (bus 14), so you may be able to use that and then switch to another bus company to get you from Annapolis to Rehoboth. Sorry that I don't have very detailed informaion.

Oops. Here's the phone number for Carolina Bus company: (919) 833-3601