Your example of conversation flow sounds to me quite natural, literally translated in Bulgarian:
*Ами, добре - (quite informal - analog to "Ok, well,")
Ами, добре*, благодаря за прекрасния урок.
Ами, добре*, ще те видя (or "ще се видим") следващия път.
Пожелавам ти приятен ден!
Аз също!
Довиждане!
Довиждане!
Actually you could use most of the casual phrases (in their translations) in such conversations. Honestly I don't think there's a significant cultural difference.
PS. In phone conversations especially , most used is "Дочуване!"