I starting making soap specifically for coffee soap for my husband. He gives me feedback with every change I make, letting me know what he likes and what he doesn't as well as concerns he may have about the possible staining of the shower stall. In fact the possible staining was his first concern. He was afraid I'd hate having to clean the shower stall. But it doesn't stain.
Anyway, the finer the grind of coffee, the better. It can be rough on the skin otherwise. Some body parts don't so much like scratchy exfoliants. But he does like the exfoliant action as well as the mere idea of coffee in his soap.
I have made coffee soap with spent grounds (dried in the oven to remove all wetness prior to adding to the soap) as well as with unused grounds. For unused grounds, I use de-caf because my husband won't drink de-caf and every hotel room in the country seems to always put at least one or two packets of de-caf in the room if they provide a coffee pot.
As far as it coloring the soap or bleeding color, well it does a bit, but not as much as one would think, especially if you use spent dried grounds. For color, I used tea or liquid coffee in place of water in the lye solution. Or if I want really darker brown coffee soap, I use cocoa powder. I have made light colored coffee soap (with tea water) all the way to chocolate brown colored coffee soap (with cocoa powder).
Also, I recommend using only a tablespoon or two of coffee grounds per batch to start. You don't really need a lot to create a nice coffee soap.
And btw, if you want it to smell like coffee you will need a nice fragrance oil to obtain a soap that smells like coffee. But make sure to check if it is a discoloring FO and adjust your plans for that. For example, don't add the discoloring FO to the portion that you want to be lighter in color.
Here is a link to an informative article about using coffee grounds in soap:
https://www.soapqueen.com/tag/coffee-grounds/