I have a couple of suggestions for you. The first is when you go back, don't actually sew all the way back off the bias tape. Use the wheel instead of the foot control and make sure that last stitch stays on the fabric (you might have to lift the presser foot and move the fabric a bit to make that happen). Then go forward again. If that doesn't work, you might try using a "Jean-a-ma-jig" or "Hump Jumper". I have a Jean-a-ma-jig and it does come in handy. But you could make something simple yourself that will do just as well, which is what I often do because I keep misplacing that little piece of plastic. You can fold a couple of pieces of cardboard and place them on either side of the seam at the back of the presser foot and just under the ends. Then do your backstitch and then go forward. Every machine is different and yours just may not like sewing on air, in which case my first suggestion would be your best bet, or a combination of both suggestions.

Here is a link that might be useful: Jean-a-Ma-Jig

The feed dogs are causing the tape to hang up--why not slip a piece of paper or stabilizer underneath the tape end and then tear away? I think this might help.

I use small pieces of newsprint paper in cases like that. You can buy big pads of it in the art dept at hobby stores. It tears really easily.

Layer the fabric and then the tape/ribbon and then the paper on top. Paper makes everything easier! And I do almost all my sewing with my walking foot, that helps too.