Today you can get the bookmarks and apply a bookmark throught he javascript API:
https://community.tibco.com/wiki/tibco-spotfire-javascript-api-overview#toc-20
However it would also be great to create new bookmarks, in this way when embedding a spotifre page into your webpage you can give the user the ability to store the (page, markings and filters etc.) Spotfire view that he currently has. And afterwards you can direct the user back to this page.