bookmark-jump-other-window which you can clone and modify to create the function
(defun my-bookmark-jump-other-frame (bookmark)
"Jump to BOOKMARK in another frame. See `bookmark-jump' for more."
(list (bookmark-completing-read "Jump to bookmark (in another frame)"
(bookmark-jump bookmark 'switch-to-buffer-other-frame))
Bind that function to a key chord of your liking and use it to open bookmarks in another frame, e.g. like that:
(global-set-key (kbd "C-x C-5 b") 'my-bookmark-jump-other-frame)
my-bookmark-jump-other-frame still needs
bookmark.el and its functions. Make sure the appropriate functions are loaded in your startup file, e.g.:
(autoload 'bookmark-completing-read "bookmark"
"Prompting with PROMPT ...[rest of docstring (optional)]")