BPBible

What you can do is create a new Topic List (go Bible > Manage Topics). Call it something like Bookmarks. Then you can select the verse you are up to, and tag it with Bookmarks (press t or right click and select Tag Verses, and then select Bookmarks). To get back to it later, go Bible > Manage Topics and open the bookmarks list and go back to where you were up to.

Also, it should remember where you were up to when you quit and come back to it when you reopen it.