Sarah,
I was always worried about people like dentists suspecting my drinking. Lots of people have bleeding gums and I'm sure you'll be fine. I wondered too about all the sugar I drank in the alcohol but my teeth turned out to be okay. I have developed a phobia of doctors after I received scary news regarding my drinking but I am also looking forward to going in the future and telling them honestly that I don't drink anymore.
The dentist sees all types of teeth in various conditions. I'm sure you'll be fine!