I have three bookmarks configured in ArcMap, but they are not showing up in ArcPad after "Get data for ArcPad" and subsequent form management in ArcStudio.
I have just successfully observed my bookmarks come across to ArcPad from ArcMap after check out. Am using ArcPad 10.2.5 and ArcMap 10.7. See screenshot with the two bookmarks in each.
You also mention form management in ArcPad Studio. What changes are you making in ArcPad Studio? Bookmarks are saved in the APM. Do you see the bookmarks there?