First off, check the weight of the bat. Can you hold it out in front of you with one hand for at least one minute without it feeling too heavy? If not, try out a lighter bat.

If your bat is the right weight, know that strength, speed, and resistance training all increase bat speed. Try strengthening your arms by lifting weights. Core stability training will also help to transfer power mid-swing from your back side to your front. You can also have someone hold the bat back as you swing, which will force you to swing against the resistance (this should be done routinely).

You can also do certain drills that focus on speed, like the one-handed drill (use your top hand and your bottom hand separately before having two hands on the bat). There are also a bunch of tools out there, like the Thunderstick Training Bat (basically a weighted rod), that will help with bat speed and hand-eye coordination.