Value of joystick reduces when I send it over serial
A fundamental lack of understanding of how serial communications works is what you have.  

Serial sends bytes. You are attempting to read an int. The two don't match. Not only that, but you are sending the value as text, not a number, so you're interpreting it as gibberish.

My suggestion: do the map on the master not the slave, and send a raw byte between 0 and 255 not a string of text between "0" and "1023".

bluetooth.write(map(yVal, 0, 1023, 0, 255));