AoiAR:
What I want to do is similar to a remote keyboard, I don't want to mix USB with BT
There are BT Radios which are designed for the HID profile. You should be looking at one of those. It will significantly reduce the amount of code you have to write (and your Arduino has to run.)
Such as this one:
AoiAR:
As for the power issue I was searching a little and saw this:In the Atmega328 datasheet:
Power Consumption at 1MHz, 1.8V, 25°C
– Active Mode: 0.2mA
– Power-down Mode: 0.1?A
– Power-save Mode: 0.75?A (Including 32kHz RTC) (0.00075mA)
So active mode of the ATmega328 by itself is drawing 0.2mA @ 1MHz. Keep in mind that none of the Arduino libraries support 1MHz natively. So you'll have some re-working ahead of you if need to use anything timer-based (millis, delay, pwm, spi communication, etc.)
AoiAR:
And from Energizer cr2032 datasheet (3V 250mAh Li Ion button cell battery) :
with a load of 68,000 Ohm, drains 0.043 mA for 721h (30 days) at ~3V
So what? What do you care what the life is at 0.043mA? Look at the graph right below that one, "Pulse Discharge Characteristics." Continous drain at 0.2mA is 225 Hours. The battery can withstand pulses into the 5-7mA range for up to 2 seconds, with a drop down to 2.8V. So life in a 5mA "pulse" application (sleep-wake up-sleep) is 200 Hours or so (8 days).
AoiAR:
But my application only needs non continuous transmission so the chip would be in power save or power down mode most of the time.
You are completely focused on the wrong component. The bluetooth radio is what will require large current consumption, not the tiny ATmega328. The HID Bluetooth module I linked to above has current consumption in the range of 12-40mA.
Getting an ATmega328 to run on a coin cell is certainly possible (not an Arduino board, but just the micro). Running a (relatively) high power RF radio off one? That's an extreme challenge.