could you post a picture? before attaching to a garment? generally, straps (tubular, im guessing) should be pinned at one end, and fed through the tube. i usually use a giant safety pin, or a paper clip. a paper clip makes a small hole, and doesn't poke through and stab you! just pin one side of the tube, and stick the paper clip into the tube. slide the fabric toward the end, holding the paperclip inside the tube. sort of like rolling down a sock over itself. i have never heard of an apron shirt, but that is how i make straps for other things.
Hmm... hard to write this out without actually just showing for my straps, I use same technique for drawstrings. That's folding in each edge a little (enough for the sewing machine to grab) then folding in half and stitching.
The best and easiest way is to use a bodkin. Sort of like using a safety pin but IMO faster. You can find them in any fabric store. It's just a small rod with a ball on one end and the other end is flat with a slit in it. I guess some people slip the fabric into the slit to secure it before they pull back through the strap. I think that's a pain in the butt. I use a safety pin through the slit and attach the fabric that way so it doesn't slip off. If I didn't use this I would have stopped making apron shirts a looong time ago.
