Mimi do you have a steam system(which would be very old)or a hot water system? in a hot water system you shouldn't have to bleed after you get water from the bleeder valve. O steam system really shouldnt need much bleeding at all because stem is a gas like air ( which is what you're trying to bleed out)and will push the air through the system. as the steam cools in the system it condenses and trickles back to the boiler in the return pipes by gravity.If you have a steam system you should have large ( at least 3" in diameter) pipes in the basement with a collar every so often where the radiator supply and return connect.I just recently replaced a steam system in my house with a hot water system and had to replace all that large cast iron pipe with 1-3/4 inch copper. Also if you have a steam system there will be a bullet shaped relief valve on each radiator.
These are in case of overpressure in the system.
Why are you blleding the radiator anyway? No heat?
Better take it up with your landlord.