A hat? What classes are you showing in? What kind of a show is it, AMHA - AMHR - Open Show - Pinto Show? Navy blue is a classic color for bays as you do not want to take away from the horse with loud colors - browns/tans/beige are nice too with bay horses. Let us know what classes and type of show you are showing in, so we can help. Yes, on the black pants and boots.
OOPS. sorry I reread your post. I see now about the hat for trail and showmanship. Showmanship is about you, then the horse is a prop so to speak, so were something that compliments the horse - beige/white/brown/taupe those kind of colors, with hat, boots to match. On the dressy side. Trail, maybe not as dressy looking but you can certainly wear the same thing you wore for showmanship.
You could wear Reds - they look good and the right color of bay I love PINK with them. But again showmanship is about you, so wear something that looks good on you and blendds nicely with the color of the horse. An - easy on the eyes outfit. Gee hard to explain