Because the you have to hit a ball to get on base with your bat making it a baseball bat because those three words combine together to make that one word.
This also depends of your own preference. Most people choose the bat that feels best in their hands and how the weight is distributed through the bat. Top of the line bats include- Denmarini Voodo...
At Bat- A turn trying to get a hit, every time you go up to the plate to try to hit, it counts as an at bat, unless you get hit by the pitch or you do a sacrifice bunt or fly out.