Most commonly I'd say "on my way home." Usually when you add 'to' it's more for when you are going to a specific place: "--to the store", "--to a festival", "--to my grandma's house". When you're talking about just going in a direction you don't use the 'to': "on my way south", "on my way downtown", "on my way up". In this case, think of "home" as a direction.