Silicone brushes are the best thing to happen to barbecue since the charcoal briquet.
I long ago relegated my natural and nylon bristle brushes to cleaning computer keyboards. Silicone brushes load up with lots of sauce, deliver it evenly, and are easy to clean and decontaminate.
They are dishwasher safe. We have three at my house: One for barbecue, one my wife uses for egg washes and other baking, and one for other uses. There are many brands on the market but I especially like the angled head of this model for applying BBQ sauces.