HC05 Communication Issue

The first use of mySerial.read() is pulling the 'b' from the buffer and will not be there for the second reading.

Try

 if (mySerial.available())
char val = mySerial.read();
   // Serial.write(mySerial.read());
  Serial.write(val);

 // if (mySerial.read() == 'b') {
if (val == 'b') {