Bana bir bardak getirebilirmisin lütfen?

Could you please bring me a cup?

Thank you

Correct.

However, If you make a politer statement, you can add "-iz " in the end of question word "misiniz" , if you are asking this from a person whom you don´t know , then its better to make it plural ---> "misiniz ", so you don´t have to use "lütfen", as you made the statement "politer" by adding -iz  [misiniz]

Bana bir bardak getirebilir misiniz ?

Tunci thank you so much