Right you need to wear a hat of some form for inhand, velvet riding hat is perfectly acceptable, as is a beagler or a trilby. I wouldnt reccomend a girl wears a bowler or a flatcap.
Most local shows require you to have a hat marked upto safety standard when either handling or riding on the show ground.
I personally wear my velvet show hat
I wear a trilby - just prefer it and my little cob is not badly behaved so don't really need a hard hat. My hair is in a bun and netted just on the bun rather than a hair net under the hat, which you would with a riding hat.
If you really want to be correct with a hard hat it should be navy or brown. To be really correct for in hand it should be a beagler - no harness, but don't worry it yours is harnessed, if it is flesh coloured harness that is more acceptable.
I personally did not want to go to the expense of an in hand hard hat, and as I am showing a traditional, my trilby really does the job - it was about £20 off e-bay.
This is my show turnout with Stinky - ignore the washed out look - I had a good night at the BSPA with a bottle of wine and a BBQ night before.
I wear brown very comfy joddie boots to allow me to run him out - he really gets a move on. If he had dark legs I would be wearing light trousers.