I have used this half square triangle method, but used bias strips to start with, so i didnt end up with bias on the units outer edges.

Bias has never been a problem for me. I guess I use tacks to keep it in place so no problem with it buckling in the middle or stretching out of place. If you put a pin in the center of the seam that will help also to keep it in place. I never pay any attention to bias.