Several years ago, I made this quick tutorial to help out a long-distance friend who was making a Blazblue costume. I figured it might come in handy for others, too, so here we are.
Note: It's probably best if you know how to do straight bias tape and outer corners first, since those are much easier. There are many tutorials available on the internet, including some by me, which will show you how to do these.
Step 1: Gather Your Bias Tape and Fabric.
Similar to the process for applying bias tape to an outer corner, the first step is to line your strip of bias tape up and sew right up to the point pictured above. Fold your bias tape so that it makes a 90 degree angle, and sew up to the point again from the other side. Be precise!
Step 3: Flip and Clip.
At this point, the back of your fabric should look like this. CAREFULLY clip to the point at a 45 degree angle. Do NOT cut the bias tape, just the fabric you are attaching it to.
Step 4: Topsy Turvy.
The next part is the most difficult to visualize, so I included quite a few reference pictures. Take both of your bias tape edges and put them together, so that the length of the tape is running in a straight line. It should look more or less the same on both sides. The picture taken from the bottom should help illustrate how it's
folded--the seam allowances should all be facing away from the strip of bias tape. Pin them in place!
Next, take a ruler and extend the line diagonal line formed by the blue fabric on down as if it
continued through your bias tape. (This is the lightly penned diagonal line.) Then, draw the angles like you would for an outer corner, but in the formation pictured above. The folds in the bias tape are making it try to close back in on itself in the picture (and resultingly skewing the proportions a bit), but all the lines should be a straight shot from point to point.
Stitch along the line as shown, then clip excess fabric.
Flip everything to the inside.
Congrats! You're done. Finish the back with your method of choice. (Slipstitching, glue, topstitching, etc.)