Thanks for the quick reply, bobj3. The router is specified as having a 1/2" collet with only 1/4" adapter (no 3/8"). Unfortunately, I don't have a caliper handy right now, but I will check the ID of the sleeve. Anyway, going against my reluctance, I managed to pull the sleeve out with pliers without much effort. Now, the bit slides into the sleeve. It's a very snug fit, leaving scratch marks on the bit shank.
So, now I have three questions:
1) For safe operation, much of the shank needs to be inside the sleeve. The bit I was using has a shank length of 1-1/4" and the tapered sleeve is 3/4" long. More the shank is inside the sleeve, the harder it is to pull the bit out.
2) Will it wear out the sleeve and/or inside wall of the spindle if the the sleeve comes out everytime I pull out the bit?
3) How far in should the sleeve sit inside the spindle?