I use GIMP rather than Photoshop, but I'm sure concepts are basically the same. Bucket fill requires you to have first selected the
area you want to fill, and the most obvious quick way to do that would be to use select-by-color to select the background, but this can be tricky/impossible to do acceptably depending on how different the background color(s) are from the coin.
The other alternative, rather than select-by-color, would be to cut around the coin either manually (GIMP has "free select") or with any kind of smart select/cutting tool that Photoshop provides. You don't need to follow every pixel-by-pixel nook and cranny of the edge of the coin - just zoom in to the point that you can make selection points that link sections of the edge that - at that level of zoom - are roughly straight.
As a third alternative, there's a website, remove.bg that I recently heard about that will automatically remove the background from various
types of photo (not just coins) for you. There's a free tier of service and a paid one. You can at least try the free tier to see if you like the results.
https://www.remove.bgBen