If you would like to have your hair and/or makeup done on the wedding day, I recommend using Notino app to book an appointment in Budapest. There is an option to choose English-speaking artists.
A beauty salon I can recommend is A-list Salon & Spa. There are two locations, one in Buda and one in Pest. You can make a booking through their website.
Alternatively, we can help arrange a hairstylist and makeup artist for you. Please let us know in advance if you are interested so we can coordinate the timing and details.