How to estimate the peak power of BLE?
You probably should rely on average power instead of peak power, unless you want to use full power all the time (BLE typically is used to send small packets of data and sleep most of the time). 

Have you seen this or similar video? 
https://youtu.be/nyWMaAF4dRQ

It shows how other wireless modules consume energy (average is very small compared to peak and it depends a lot on how you use module). 

Maybe just take some small battery with known capacity, repeat (and count) data transfer operations until battery discharges completely, or discharges to some voltage.