This brush is really meant for your vanity, not day to day purse travel. I have no issues with the cap. If you are traveling I assume you are taking other brushes as well. The cap will stay in place just fine in a brush roll keeping any residual lip color from contaminating other brushes. For everyday purse carry get a retractable lip brush.
Basically, it comes with a cap, but the cap is not made well. It snaps on, but you have to put it on a certain way so as not to fray the brush and ruin it. I'd say, tape the top in place so that it doesn't twist around.