Here is another way....
Determine the diameter of the fat end of the bat.
Determine the diameter of the handle/end of the bat
Mark the center of the bat's fat end. You will use this for a visual check later.
Take two 2x4s about a foot longer than the bat and screw them together along the long edge to simulate a piece of angle iron.
Take a square piece of ¾" plywood, about 4" square and cut a hole in it for a snug fit on the bat handle
The center of the hole will be from two adjacent sides of the square with a dimension of the radius of the fat end of the bat
Take a piece of scrap and screw it on the previous drilled piece to block one side of the hole off so the handle won't go all the way through.
Next fasten this piece in the v of the 2x4s on one end with the blocked off side of the hole towards the 2x4 ends
You now have a jig to place the bat in. Put the handle in the hole and clamp the fat end of the bat in the V so it won't move.
Then take about a 4" piece of 4x4 lumber, square both ends, and drill a hole thru the 4" dimension with your drill press.
Use the drill you plan to drill the bat with, and your center, from two adjacent sides, will again be the radius of the bat's fat end.
You now have a accurate drill guide to slide along the V of the jig for the drill.
Drill with your favorite drill motor.
The 2x4s could be 1x4s or just about anything around that size. You could even just clamp one 2x4 to your bench top.
Same for the other pieces. Lumber size is pretty flexible.
Alternative way:
If you have a laser pointer (put it in the chuck), or even a plumb bob you could use them to find the spot on the floor drillpress floor plate to clamp a board down that has the diameter of the bat's handle cut into it. Then put a center in the drill's chuck to hold the bat while you rotate and move the drill press table up to the bat. Clamp the bat to the table and you are ready to drill.