Connect your BUS MOUSE pins to the following pins of your Arduino Pro Micro:

• Gnd : Ground
• Vcc : Vcc (+5V)
• Port D3 : X axis encoder / channel A
• Port D2 : X axis encoder / channel B
• Port D1 : Y axis encoder / channel A
• Port D0 : Y axis encoder / channel B
• Port B3 : Switch 1
• Port B2 : Switch 2
• Port B1 : Switch 3

Upload the following sketch to your Arduino Pro Micro using the Arduino IDE (I used the 1.6.7 version for this code):

#include <Mouse.h>

/* ================================================================================
   Author  : GuilleAcoustic
   Date    : 2015-05-22
   Revision: V1.1
   Purpose : Opto-mechanical trackball firmware
   --------------------------------------------------------------------------------
   Wiring informations: Sparkfun Pro micro (Atmega32u4)
   --------------------------------------------------------------------------------
     - Red    : Gnd                          |   Pin: Gnd
     - Orange : Vcc (+5V)                    |   Pin: Vcc
     - Yellow : X axis encoder / channel A   |   Pin: PD3 - (INT0)
     - Green  : X axis encoder / channel B   |   Pin: PD2 - (INT1)
     - Blue   : Y axis encoder / channel A   |   Pin: PD0 - (INT2)
     - Violet : Y axis encoder / channel B   |   Pin: PD1 - (INT3)
     - Grey   : Switch 1                     |   Pin: PB3
     - White  : Switch 2                     |   Pin: PB2
     - Black  : Switch 3                     |   Pin: PB1
   --------------------------------------------------------------------------------
   Latest additions:
     - 2016-01-28: Software switch debouncing
   ================================================================================ */

// =================================================================================
// Type definition
// =================================================================================

#ifndef DEBOUNCE_THREASHOLD
#define DEBOUNCE_THREASHOLD 50
#endif

// =================================================================================
// Type definition
// =================================================================================
typedef struct ENCODER_
{
  int8_t  coordinate;
  uint8_t index;
} ENCODER_;

typedef struct BUTTON_
{
  boolean state;
  boolean needUpdate;
  char    button;
  byte    bitmask;
  long    lastDebounceTime;
} BUTTON_;

// =================================================================================
// Constant definition
// =================================================================================
const int8_t lookupTable[] = {0, 1, -1, 0, -1, 0, 0, 1, 1, 0, 0, -1, 0, -1,  1,  0};

// =================================================================================
// Volatile variables
// =================================================================================
volatile ENCODER_ xAxis = {0, 0};
volatile ENCODER_ yAxis = {0, 0};

// =================================================================================
// Global variables
// =================================================================================
BUTTON_ leftButton   = {false, false, MOUSE_LEFT,   0b1000, 0};
BUTTON_ middleButton = {false, false, MOUSE_MIDDLE, 0b0010, 0};
BUTTON_ rightButton  = {false, false, MOUSE_RIGHT,  0b0100, 0};

// =================================================================================
// Setup function
// =================================================================================
void setup()
{
  // Attach interruption to encoders channels
  attachInterrupt(0, ISR_HANDLER_X, CHANGE);
  attachInterrupt(1, ISR_HANDLER_X, CHANGE);
  attachInterrupt(2, ISR_HANDLER_Y, CHANGE);
  attachInterrupt(3, ISR_HANDLER_Y, CHANGE);
  
  // Start the mouse function
  Mouse.begin();
}

// =================================================================================
// Main program loop
// =================================================================================
void loop()
{
  // Update mouse coordinates
  if (xAxis.coordinate != 0 || yAxis.coordinate != 0)
  {
    Mouse.move(xAxis.coordinate, yAxis.coordinate);
    xAxis.coordinate = 0;
    yAxis.coordinate = 0;
  }

  // ---------------------------------
  // Left mouse button state update
  // ---------------------------------
  ReadButton(leftButton);
  UpdateButton(leftButton);

  // ---------------------------------
  // Right mouse button state update
  // ---------------------------------  
  ReadButton(rightButton);
  UpdateButton(rightButton);
  
  // ---------------------------------
  // Middle mouse button state update
  // ---------------------------------
  ReadButton(middleButton);
  UpdateButton(middleButton);

  // Wait a little before next update
  delay(10);
}

// =================================================================================
// Interrupt handlers
// =================================================================================
void ISR_HANDLER_X()
{
  // Build the LUT index from previous and new data
  xAxis.index       = (xAxis.index << 2) | ((PIND & 0b00000011) >> 0);
  xAxis.coordinate += lookupTable[xAxis.index & 0b00001111];
}

void ISR_HANDLER_Y()
{
  // Build the LUT index from previous and new data
  yAxis.index       = (yAxis.index << 2) | ((PIND & 0b00001100) >> 2);
  yAxis.coordinate += lookupTable[yAxis.index & 0b00001111];
}

// =================================================================================
// Functions
// =================================================================================
void ReadButton(BUTTON_& button)
{
  // Variables
  long    currentime;
  boolean switchState;
  boolean debounced;
  
  // Get current time
  currentime = millis();
  debounced  = (currentime - button.lastDebounceTime > DEBOUNCE_THREASHOLD);

  // Get current switch state
  switchState = !(PINB & button.bitmask);

  // Button state acquisition
  if ((switchState != button.state) && debounced)
  {
    button.lastDebounceTime = currentime;
    button.state            = switchState;
    button.needUpdate       = true;
  }
}

void UpdateButton(BUTTON_& button)
{
  if (button.needUpdate)
  {
    (button.state) ? Mouse.press(button.button) : Mouse.release(button.button);
    button.needUpdate = false;
  }
}