Look at the second picture first.
Press flat all along the bias strip. If you are doing a stem with any curve in it you can use your pattern as a guide to curve the stem now while you are pressing. Cut the bias strip to the length you need it. Stems typically end up under another applique piece so there is no need to finish off the edges. I tried using the scraps of fusible web on the back of my stems to hold them down on the background fabric ...I had mixed results. The fusible web held down part, but not all of the stem. I guess it was enough to hold it in place mostly but I still felt I had to adjust some parts that seemed to have moved over a bit.