The trick is to put it on the cone and then roll the grip back up. Place the rolled up grip on the cone and then put it onto the bat.
As for your bumps, the easiest thing is to roll the grip up and down until its flat. You'll stretch the grip in process but ti should be easy enough to push down. There is a technique but I can't really explain it but it basically involves rolling the grip back on itself to reposition it. Other than that you'll just have to push it down using your thumbs.
I can put a grip on in about 15 seconds.....