I do a fair amount of bobber fishing on the Sandy and at times the wind can be really heavy. A couple things you can try that have worked for me are.......
You say you're using a braided line, make sure it's one that will float (i.e. Fireline, Namofil, etc.) and not to heavy, 14# to 17# is plenty.
When it's windy, I leave my line on the water as tight between the tip of my rod and the float without creating any drag or push if possible. To mend, just lift the line of fthe water and reset.
Much like when side drifting, when your bobber goes down or stops don't set the hook sort to say, simply lift to create tension on the line and if you feel a headshake give a little pop to drive that hook home. No need to swing for the fences as the fish will hook themselves anyway......
Hope that helps you out.....