Originally Posted by Prism99

I would starch the fabric before cutting, cut on the straight-of-grain, sew the strips together, starch again, and then trim to the correct dimensions. Starch is necessary to stabilize the fabric so that the bias edges do not stretch out of shape and distort.

This would be my preference over cutting bias strips. It's possible to sew a bias edge to a bias edge, but only if you have heavily starched the fabric (1:1 starch:water proportions) before cutting the strips. It's better to sew straight-of-grain strips together, and then have to deal with the bias only on the outer edges.

Since this is a purse, the edges do not have to match up to another block and trimming (if a bias edge stretches) will not cut off any points or other important pattern elements.