At first I thought it might not be easily doable ... but it looks like Baltimore Penn Station is just 2 miles from Hopkins' main campus and not in 'Baltimore' proper or the BWI stop.
I can bet it will be expensive though. My monthly from Philly to Newark, NJ is almost $1200. I checked you get a bargain ... $1008 a month or $448 for a week (ten trip ticket).
Hopkins is a great school though and would be well regarded on a resume so it might be worth cost/pain of the commute. Or you might consider renting out a room for when you need to be in the program it may be cheaper than the train. (sucky option but it is one)
"I'm stuck in New Jersey
I don't expect too much
If the world ended today
I would adjust"