Is the gender important for your statement?
In this case: probably no. So use the "neutral" form which is almost always the male form.
If you want to express that you are going to that type of person (or shop...) who will finally fix that rotten tooth / cut your hair / bake & sell bread... you go
"zum Zahnarzt" / "zum Friseur" / "zum Bäcker"...
Once you are not making a general statement but are talking about the individual, the gender should be correct.:
Ich gehe zu der Zahnärztin in der Goethestraße -> female
Meine Friseurin(*) hat ... -> female
There are some exceptions to the "neutral" = "male" rule: "Katze", "Hebamme" (perhaps s.o. else can come up with more examples?) use the female for general / "neutral" statements.
(*) Don't use "Friseuse" please!