Here is the code I am currently using

#include <Wire.h>
#include "I2Cdev.h"
#include <PMW3360.h>
#include <BPLib.h>
#include <SoftwareSerial.h>

// Mouse Movement Variables
#define SS  17          // Slave Select pin. Connect this to SS on the module
PMW3360 sensor;
const unsigned long accumulationTime = 10; // Accumulate data for --- milliseconds
const int sensitivity = 500;
const int DPI = 400;

// Bluetooth Variables
#define RX_PIN 9 // connect to TXD of module
#define TX_PIN 10 // connect to RXD of module (logic level 3.3v!)

SoftwareSerial swSer(RX_PIN, TX_PIN, false); // Only three arguments
BPLib *BPMod;

void setup()
{
  Serial.begin(9600);  
  swSer.begin(9600); // Set the baud rate for software serial
  BPMod = new BPLib(swSer);
  BPMod->begin(BP_MODE_HID, BP_HID_MOUSE);

  if (sensor.begin(SS)) // Initialize the PMW3360 sensor
  {
    Serial.println("Sensor initialization succeeded");
  } 
  else
  {
    Serial.println("Sensor initialization failed");
  }
  sensor.setCPI(DPI);
  //Mouse.begin();
}

void loop()
{
  float Acc_X = 0;
  float Acc_Y = 0;
  bool movementDetected = false;

  unsigned long startTime = millis(); // Record the start time

  // Accumulate readings for the --- duration
  while (millis() - startTime < accumulationTime) {
    PMW3360_DATA data = sensor.readBurst();
    if (data.isOnSurface && data.isMotion) {
      float mdx = constrain(data.dx, -127, 127);
      float mdy = constrain(data.dy, -127, 127);

      Acc_X += mdx;
      Acc_Y += mdy;
      movementDetected = true;
    }
  }

  Acc_X /= DPI;
  Acc_Y /= DPI;

  // Move the mouse based on accumulated values if movement was detected
  if (movementDetected) {
    BPMod->mouseMove(-Acc_X * sensitivity, Acc_Y * sensitivity);
    //Mouse.move(-Acc_X * sensitivity, Acc_Y * sensitivity);
  }
}

Here is the code using Serial1

#include <Wire.h>
#include "I2Cdev.h"
#include <PMW3360.h>
#include <BPLib.h>

// Mouse Movement Variables
#define SS  17          // Slave Select pin. Connect this to SS on the module
PMW3360 sensor;
const unsigned long accumulationTime = 10; // Accumulate data for --- milliseconds
const int sensitivity = 500;
const int DPI = 400;

// Bluetooth Variables
// Bluetooth Variables
#define RX_PIN 0 // connect to TXD of module
#define TX_PIN 1 // connect to RXD of module (logic level 3.3v!)

Serial1 swSer(RX_PIN, TX_PIN, false); // Only three arguments
BPLib *BPMod;

void setup()
{
  Serial.begin(9600);  
  Serial1.begin(9600); // Set the baud rate for hardware serial
  BPMod = new BPLib(Serial1);
  BPMod->begin(BP_MODE_HID, BP_HID_MOUSE);

  if (sensor.begin(SS)) // Initialize the PMW3360 sensor
  {
    Serial.println("Sensor initialization succeeded");
  } 
  else
  {
    Serial.println("Sensor initialization failed");
  }
  sensor.setCPI(DPI);
  //Mouse.begin();
}

void loop()
{
  float Acc_X = 0;
  float Acc_Y = 0;
  bool movementDetected = false;

  unsigned long startTime = millis(); // Record the start time

  // Accumulate readings for the --- duration
  while (millis() - startTime < accumulationTime) {
    PMW3360_DATA data = sensor.readBurst();
    if (data.isOnSurface && data.isMotion) {
      float mdx = constrain(data.dx, -127, 127);
      float mdy = constrain(data.dy, -127, 127);

      Acc_X += mdx;
      Acc_Y += mdy;
      movementDetected = true;
    }
  }

  Acc_X /= DPI;
  Acc_Y /= DPI;

  // Move the mouse based on accumulated values if movement was detected
  if (movementDetected) {
    BPMod->mouseMove(-Acc_X * sensitivity, Acc_Y * sensitivity);
    //Mouse.move(-Acc_X * sensitivity, Acc_Y * sensitivity);
  }
}