It will take time
This exactly. If your horse won't work properly with a bit in its mouth, I don't think you have much hope of wanting to do bridleless riding YET. Get the horse going well with full tack, and then start using your reins as little as possible, but still have them there just to reinforce your cues at first.
I "taught" my mare to move off of a tap on the base of the neck-so, if I wanted her to go right and she wasn't immediately responding to seat and leg, I would tap the left side of her neck with my finger. Before she got laid off, we had an awesome whoa-I only needed to sink my back down, push my feet forwards a little, and she'd stop dead. Bridleless stops are a little more shaky now (it takes her 4 or 5 steps instead of 1) 'cause I haven't been on her in a while, but I don't think it'll be too hard to get her back in form. Anyways
, I'm rambling...the point is, get your horse going perfectly with a bridle before you start considering without. As others have said, bridleless/tackless riding is just a by-product of good training. It's not generally something you specifically train for.