Dirt in a horse's coat can be a good thing--it is natural protection from insects and sunburn, and it exfoliates the skin.
If you are planning to show (it sounds like you are), I would recommend finding a nice cotton sheet to put on her after a bath until she is completely dry. Horses try to replace the dirt in their coats that were lost in a bath, and the sheet would protect her from some of that. Be sure not to bathe her too often, because you could strip her coat of its natural oils and make it appear dull.
Beyond that, a daily rubber curry and brushing will do wonders...I rarely have to bathe my guys to keep them looking clean.