When you log into Chrome and set a bookmark, that bookmard is available to you no matter which machine you are using. The bookmarks stay with your account, not the preferences on the machine. This is a good thing. If your computer crashes or you have to create a new computer account, all your stuff on Chrome will still be there! The same is true for your history and your people.
To see the bookmarks you’ve saved, you may want to turn on the bookmarks with View->Always Show Bookmarks Bar or else you can just use the Bookmarks to show all bookmarks.