Finishing telephone conversations
When I'm talking to my tutor on Skype I'm not sure how to finish our conversation. In English I often use a polite series of phrases or endings to draw a conversation to a close. It goes something like this:

(A conversation has happened)
Me: Ok, well thanks for a lovely class. (this indicates that I'm happy to finish the conversation here. It gives both parties time to bring up anything else they urgently need to talk about)
Tutor: Ok, well I'll see you next time (Their response indicates that they too are happy to end the conversation)
Me: Hope you have a nice day (Some general pleasantry)
Tutor: you too (their response)
Me: Goodbye
Tutor: Goodbye (The conversation has now finished and I can safely hang up without causing offence)

Is this kind of politeness necessary in Bulgarian, and how might this scenario go in Bulgarian?

Many thanks,
Joe

Question

Finishing telephone conversations
When I'm talking to my tutor on Skype I'm not sure how to finish our conversation. In English I often use a polite series of phrases or endings to draw a conversation to a close. It goes something like this:

(A conversation has happened)
Me: Ok, well thanks for a lovely class. (this indicates that I'm happy to finish the conversation here. It gives both parties time to bring up anything else they urgently need to talk about)
Tutor: Ok, well I'll see you next time (Their response indicates that they too are happy to end the conversation)
Me: Hope you have a nice day (Some general pleasantry)
Tutor: you too (their response)
Me: Goodbye
Tutor: Goodbye (The conversation has now finished and I can safely hang up without causing offence)

Is this kind of politeness necessary in Bulgarian, and how might this scenario go in Bulgarian?

Many thanks,
Joe

Answer

maybe the end of your conversations would look like this: 
You: Благодаря за хубавия урок! Желая ти приятен ден
Tutor: Подобно! И на теб хубав ден!
You: Дочуване!
Tutor: Дочуване!

Answer

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!"