I'd like to make RC car and remote controller via bluetooth (HC06)
There are some fundamental problems in the code - bufferPosition never stops increasing (until it reaches 32768) and so buffer will overflow. However, neither of these two problems are causing the 'trash', as you are outputting the result of reading the serial, not anything from the buffer.

The problem lies in the casting of the result from BTSerial.read() to unsigned char.

Serial.print() does not like this. Actually it doesn't care, but it won't give you what you expect. It just prints out the value stored - so 'a', which is 97, will come out as '97' on the serial monitor. Serial.print() only outputs ASCII characters when you give it a char or char[].