How do you adjust the chuck on the drill to fit the drill bit?

Depending on the size or the bit and the chuck, you can use a "collar " on the bit. Make one out of something that will slide firmly onto the outside of the bit. like the plastic tube from inside a ball point pen, a piece of aquarium tubing, etc. You can also buy 1/4" shank bits with small diameter ends. They are made to use in power screwdrivers, but will work in your drill. Hope this helps !

ANS 2 -When I have this situation I use a 'pin drill' which is essentially a 1/4 steel tube with a 'collet' on the business end that holds tiny drill bits. -I simply fit the shaft of this 'pin drill' into my bench drill's chuck.