i don't know about bus, but you can take rail all the way to manhattan, but you will need to transfer a couple times.
from PHL, take the septa regional rail (the R1 train) to 30th street station in philadelphia. from there, get on the R7 rail line to trenton, nj.
at trenton, you need to buy a NJ Transit rail ticket to go to penn station in manhattan.
at penn station, you'll have access to the 1,2,3,a,c and e subway lines.

www.septa.org
www.njtransit.com