On a bridgeport on the bottom of the quill there is a silver ring that the spindle nose goes through. If you lower your quill about 1 1/2 inches, you will see the joint between the ring and the rest of the quill column. On the bottom of this ring, by the spindle, there are two holes for a spanner wrench. You need either a spanner or some sort of post type tool to loosen this up. However, there is a hex set screw to loosen on this ring before it loosens as I recall. Loosen this ring up and spin it off.
You will have an open part of the quill. On this part you will find another set screw that you loosen out of the hole. Under this is your key for your collett keyway. Get this out and check it, the end is usually square as I recall. If it is either square or round, check it for burrs that may impeed the collett from catching properly by checking it on a collet keyway.
Put it back in, have a collett in the nose to help set the depth of the drive key. I usually make it catch, bottom it out on the colley keyway then back it off so things move freely and there is plenty - but not too much clearance.
Check it over than re-assemble. Your first set screw that goes in after you set the key depth should fit set against your key, but check to be sure you did not re-advance the key further by re-checking the collett. The rest is simple re-assembly.
Probably clear as mud, but may work for you.