ABS only works when it's needed to under hard braking, otherwise it does nothing. When the controller is in bypass mode, you have a direct link between the brake lever and caliper action, or simply stated "normal braking." If the ABS system is inadvertently activating or a valve is stuck, your brakes will actually be stiffer with less braking force.
If manual bleeding removes a few air bubbles, either you have a leak somewhere or you're boiling your brake fluid (unlikely unless you race).
If the brake lever sinks to the grip, but no leak can be found you may have a bad master cylinder (bad seal).
However, if the grip just feels mushy in general, you may want to consider some stainless steel brake hoses to stiffen up the general feel. Regular brake hoses flex quite a bit when you apply pressure and the longer the hose, the mushier the feel.