There's nothing to travelling with a brush. I simply bring it and a small tube of shaving cream (or a tiny plastic container with a teaspoon or two of the stuff).

You can work the lather in the palm of your hand easily. But I bring a little china saucer/bowl. As for drying the brush - just rinse the thing out with water and shake it dry. This gets rid of nearly all the water in seconds. You can detect a bit of moisture in the brush, but it doesn't matter. Toss it in your travel bag or leave it out to dry on the counter. It takes no time at all.