Based on the Rehoboth Beach Transportation website, it seems there are a number of options; the site does mention buses, including charters, but it does not explain every place those buses go. I enclose the link to the website so that you can contact them directly.
DC2NY has started a bus service, departing on Friday afternoons, Saturday morning, and Sunday morning and returning on Saturday evenings and Sunday evenings.
There is a bus from Baltimore to Ocean city (Greyhound) then you can take local bus 208 from Ocean city to Rehoboth
Atlantic City, NJ if you take the US 9 toll ferry. From there you can take the NJ Transit Service to Philadelphia to connect to many other trains.
You can't. The only train station located anywhere close to Delmarva is the Wilmington DE Amtrak station. You could get on the Amtrak in Newark or Harrison and travel south to Wilmington, but from there you would have to drive. You go down DE-1 towards Dover and keep on that all the way to the state line, and from there you would be in Ocean City Md.
Dwight - Amtrak station - was created in 1891.
Norman - Amtrak station - was created in 1909.
Kissimmee - Amtrak station - was created in 1883.
Alliance - Amtrak station - was created in 1990.
Hanford - Amtrak station - was created in 1897.
Gilman - Amtrak station - was created in 1986.
Wasco - Amtrak station - was created in 2006.
Fargo - Amtrak station - was created in 1920.
Anniston - Amtrak station - was created in 1926.
Palatka - Amtrak station - was created in 1909.