I'm not sure that Logic allows you to automatically bounce segments between markers. In most DAWs, markers are just meant as named, to mark sections, not to denote segments. I think Reaper has the ability to convert markers to segments (or some other word they use) and then export those segments, but I don't believe Logic has that feature.
The way I do it in ProTools, and i know it works in Logic as well, is to use markers, and then highlight the area between each marker and bounce the current selection. It's annoyingly manual, but it works fine and doesn't really take all that long