You should always push the piston back with the reservoir either cracked open or with the top off, just do it slowly so it doesn't overflow. If you have a mushy brake you have air in the lines, which you most likely know. If you have a MityVac pump you can bleed the whole system without any bubbles in a few minutes (assuming you don't let the reservoir go dry). If you're doing it the long way by cracking the bleeder, topping of the master cylinder, and repeating, it's really easy to get air in the lines if you let the master cylinder go dry. Did you bleed the master cylinder at the bars first and then the calipers or just the calipers?
You just have to keep bleeding until you get the bubbles out. Easiest if you take the calipers off the front wheel and hold them up by the bars (I personally use a bit of wire around a grip to do so), then you're letting the bubbles float up with the current and the force of the fluid to push them out even quicker.
2014 CBR500R (ABS)
2016 GSX-S1000 (ABS)