With pivot set to '3D Cursor', assuming the length of your baseball bat is in Z, and with the 'Loop Tools' built-in Add On enabled ...
- Select a transverse edge loop near the bottom of your tape winding
- ShiftS 'Cursor to Selected'
- Select a vertical set of vertices spanning the height you will want your spiral
ShiftD duplicate that span (in real life,
right-click to leave it where it is, on the surface of your object)
W > Subdivide the selection. In the tool region, adjust the count to create as many vertices as you will eventually want on your spiral... (total turns * vertices per turn).
With the vertices in the profile selected, use W > Loop Tools > Space to distribute them evenly along your profile.
O .. switch on Proportional Editing. Set the Falloff Type to 'Linear'... Select the bottom vertex of your profile alone ... hit RZ. Using the scroll-wheel, adjust the range of your proportional edit to include the top vertex of your profile.
With each wind of your mouse around the 3D cursor, you will introduce a new turn on your spiral, conforming to the surface of the bat.
Instead of doing this interactively, you could assign a Simple Deform > Twist modifier to the profile, which does the exact same thing. Set Axis to Z, and Angle set to 360 * your number of turns. That way you can go back and adjust it later, if you need to.