Then you already have everything you need — it's in your messages.
Tap the link in it — that's your personal booking page. It opens on a welcome message from your salon, and you can ask for a time right there.
Ask your salon to send it again — it takes them one tap. Your link is personal to you, so we can't recreate it here.
Prefer an app? Get Schedalize and enter your salon's invite code — same account, same conversation.