For most patients, there are no restrictions following a Botox treatment. Sometimes patients will use cold compresses immediately after injection to prevent or lessen swelling and bruising but wearing a hat typically does not present any issues.
I am an equestrian and a dermatologist, have Botox treatments now and then, and I ride 4-5 days a week, so I am quite familiar with your dilemma. I see no reason for concern or delay. Wearing a helmut that fits properly and not excessively tight should not affect your treatment significantly even the same day.