Verify first that your joystick does give you a full range between 0 and 1023 and 512 in the middle, when idle
If so then try this code
void loop() {
int analogValue = analogRead(A0) - 512; // 0 at mid point
if ( abs(analogValue-lastAnalogValue) > 1) { // have we moved enough to avoid analog jitter?
if ( abs(analogValue) > 4) { // are we out of the central dead zone?
MIDI.sendPitchBend(8*analogValue, 1); // or -8 depending which way you want to go up and down
lastAnalogValue = analogValue;
}
}
}
Note that you can pass something between -8192 (maximum downwards bend) and 8191 (max upwards bend) and center value is 0. As we have a analogValue Between -512 and +511, multiplying by 8 just gives you half the range. You could multiply by 16 if you want
(Typed here from my mobile so totally untested)