Ya gotta start with a clean bore, then swab it well with light body oil.
Regardless of caliber you dont often do well with a bullet, they are too long and create too much resistance (ie, hard to drive through). A 'round ball' (a buckshot size or sinker, or for larger calibers, a real muzzleloader RB) works well.
Lube it too, set on the muzzle, tap in with a clean soft face hammer and from there down a short ways a 'short starter' rod, then the full rod.
Regarding rods, You should use a rod that is about bore dia. for strength, and with a 'soft surface' to keep from bonking the rifling. I have a number of steel rods Ive collected; I wrap the rod with tape to soften it. The drive end needs to be solid, not threaded as a cleaning rod has. If you are using a cleaning rod you need a (preferably) brass button screwed in there. Many rods are 8x32, but 22 cal. rods may be slightly different. Thing is you need a brass screw to put in there and spin the head to be a clearance fit in the bore. Just chuck the screw up in an electric drill and use a file to reduce dia. and if needed, flatten the head. As you can imagine, this rod will not damage your bore while driving a slug through.
DO NOT use a wooden dowel. They flex and are not solid enough, the absorb too much of the impact needed.
Keep the rod pressure on the slug (ie, dont 'slide hammer' with the rod) and tap it through. Be sure to have a clean soft cloth to catch it when it comes out.