When I showed at Devon in the Amateur Handler in 1999, I wore a light brown pants suit, my paddock boots and a modest straw hat. I have been around the breeding rings for over 20 years and I like to see women handlers wear nice pants and a jacket, although these days women wear chinos and a shirt. If you notice, the men usually have on jackets and ties, and I think the women should also be appropriately dressed.
Just my 2 cents
I tend to wears khakis/slacks and a nice well-fitting sweater at the smaller shows and pull out slacks with a jacket for the bigger shows such as Devon and Warrenton.
Whatever doesn't get you more attention than your horse!
"It is the tragedy of the world that no one knows what he doesn't know--and the less a man knows, the more sure he is that he knows everything." Joyce Cary
I wore khakis, paddocks, a nice polo and a jacket, kind of mimicking the male pros. I also wore an Ariat tan visor that matched my khakis. I wore my black gloves and carried a nice crop. I can send you pics if you want. Did well, he won the Zone with little old me handling.
The dog show handlers are taught to wear a tasteful but contrasting color to show off a great topline. Or a monochromatic similar color for those where you don't want to draw attention. Never too bright, never too loose and floppy.
You don't want to wear anything that will call attention to you. All the attention should be on your horse. Conservative dress all the way. Khakis, paddocks, a nice polo or long sleeved shirt a good sports bra (nothing is worse that seeing too much movement in the breast department during the jog......) and neatly styled hair. If you wear a hat, make sure it won't blow off.
My horse won Zone champion last year with me handling her. I wore khakis, paddock boots, a nice long sleeved shirt (i.e. Ralph Lauren) and a nice straw hat (not too large of a brim). I also wore black gloves and carried a crop. In the cooler weather I wore a jacket, If your hair is long be sure to pull it back out of your face. Ditto on making sure your hat doesn't blow off or slip when jogging. Good luck!