Careful and judicious placement can sometimes help. You will need 4 "ends"- the 7" or so working part that forms the visible bow. And you'll need just a touch more for the knot- all in one piece, of course, but you may well be able to get those from the fat end of the long tie. I have just laid out a bow tie on top of a long one and in my case, I think it can be done. Then you'll need the neckband part, which can be spliced. In fact, you are going to end up with (2 each of) three sections, with a couple of seams. Go find a long tie you do not like at all and open it up carefully and see if you can't lay out your bow tie on the amount of fabric it yields. I hope you'll be pleasantly surprised.

For those who aren't keen on sewing, what I mean is this- rip the center seam and flatten out the old (donor) tie. Resign yourself to doing some piecing / seaming. You will have to cut out two bow ties and sew them together, then turn it inside out. Before doing that, though, you will have to patch together the parts. Depending on how you like to count, there are either 4 end pieces and 2 neckband pieces, or 2 left end pieces, 2 right end pieces and 2 neckband pieces. It is just that the left and right generally look the same. And, yes, you have to lay out the tie so that the stripes run at the same angle, which uses more fabric. But the neckband portion need not be blue and gold striped at all, if you run short. Just be sure you have allowed enough margin for the entire knot to be seamless and striped. There are three usual bow tie patterns, what might be called diamond end, paddle end, or butterfly. Each has its adherents and its tricks of construction. Show us a picture when you have finished, please.