Yeah, that's such a common trap (the dry broom thing). I keep a bucket of water right next to me now and dunk it every other swipe. It's a tricky technique that honestly takes a few tries to get right.
What type of broom are you using? Plastic bristles tend to work better with water than natural ones. I always wet mine lightly and sweep in short strokes to avoid scattering dust. Too much water just moves dirt around instead of picking it up. Getting the right dampness takes a bit of trial and error.