How commonly طَبِيبٌ or طَبِيبَةٌ is used in Arabic?
Is ''doctor'' used more because it's genderless?
I was wondering exactly the same. I've learned before to say طبيب for doctor, but the lessons use 'Doktor' instead. Isn't طبيب the most common way to say doctor?
The word طبيب means medical doctor, whereas دكتور can refer to either someone with a PhD degree or a medical doctor. And I suggest that you stick with طبيب for medical doctor if you want to have a good formal Arabic.
Tabeeb/tabeeba is standard Arabic, you can find it it books and stuff. Doctor/Doctora is Egyptian Arabic, we've borrowed the English word and made it Arabic. Many people these days also say "doctor" for both genders like in English. I honestly don't know if they say tabeeb or doctor in other Arabic dialects.