then click into your bundle purchase. Then on that page click on the download button next to the game you want. That will take you to the download page but you don't need to actually download any files. Once you go to the download page itself it'll show up in your library and you can install it with the itch client instead.
voxpoplar wrote
BTW if you want things to show up in your library/download with with the itch client you need to go here
https://itch.io/my-purchases/bundles
then click into your bundle purchase. Then on that page click on the download button next to the game you want. That will take you to the download page but you don't need to actually download any files. Once you go to the download page itself it'll show up in your library and you can install it with the itch client instead.