Put the cursor on the bookmark name and use C-u C-x =. Near the bottom of buffer *Help* you'll see the name(s) of the face(s) on the text at the cursor. Then M-x customize-face for that face.
I'm guessing the face you need to customize is bmkp-local-file-without-region. By default it doesn't look different from the default font (e.g., just black text).
M-x list-faces-display shows all current faces. Those used by Bookmark+ have names with prefix bmkp:
bmkp-*-mark
bmkp->-mark
bmkp-D-mark
bmkp-X-mark
bmkp-a-mark
bmkp-bad-bookmark
bmkp-bookmark-file
bmkp-bookmark-list
bmkp-buffer
bmkp-desktop
bmkp-file-handler
bmkp-function
bmkp-gnus
bmkp-heading
bmkp-info
bmkp-light-autonamed
bmkp-light-autonamed-region
bmkp-light-fringe-autonamed
bmkp-light-fringe-non-autonamed
bmkp-light-mark
bmkp-light-non-autonamed
bmkp-light-non-autonamed-region
bmkp-local-directory
bmkp-local-file-with-region
bmkp-local-file-without-region
bmkp-man
bmkp-no-jump
bmkp-no-local
bmkp-non-file
bmkp-remote-file
bmkp-sequence
bmkp-snippet
bmkp-su-or-sudo
bmkp-t-mark
bmkp-url
bmkp-variable-list
In buffer *Bookmark List*, if you use ? or C-h m you'll see their descriptions listed, showing their highlights. E.g., face bmkp-local-file-without-region shows this description with that face (same as face default, by default): Local file with no region.
UPDATE after your comment that says that you tried HH and H+, and that you want to change how a bookmark is lighted in buffer *Bookmark List*.
Bookmarks are highlighted in various ways (customizable) at their bookmarked locations (destinations).
Bookmark names/lines in *Bookmark List* are highlighted according to their types. If a bookmark has its own (destination) highlighting defined then, in *Bookmark List* a "purple flag" (face bmkp-light-mark), as you mentioned and show, is shown next to each one whose location will be highlighted (when you visit it).
In *Bookmark List*, HH turns on (destination) highlighting for the bookmark listed on the current line. H+ defines how the bookmark on the current line will be highlighted (at its destination).
There's no feature to highlight arbitrary bookmarks in *Bookmark List*. That would interfere with highlighting to show the bookmark types. (You could copy the definition of function bmkp-bmenu-list-1 and modify it to do that, I guess.)