...or you could consider using another microcontroller, one having available a module with either CPU and bluetooth onboard. The ESP32-WROOM-32U is a nice example of that.
Yes I think I should go for HC-05. I guess it is Ok to interface it with Arduino 2560 without any license, right ?. I am wondering which pins on Arduino 2560 are Tx and Rx.
You are not serious wondering about something that can be fund everywhere, particularly on Arduino's Website itself. I fear if you will ask what link...