How do I make the HC-05 bluetooth module take data from the HC-SRO4, and then send it to my Android app? Currently, I have an Arduino Uno set up, with a HC-SRO4 ultrasonic sensor printing distances of objects in front of it on a scale from 1-15 to the serial monitor. I want to attach the HC-05 bluetooth module and do the following: 
First, it will read the values from the serial monitor. Then, I would like the HC-05 module to take these numbers and continuously send it to my Android app, which will then process what to do with the numbers.

I understand the Android part may be out of scope of this forum, but please try to help me with taking data from the serial monitor and have it transmit the data.

Here is the code I have for the ultrasonic sensor:

const int trigPin = 9; 
const int echoPin = 10;
// defines variables
long duration;
int distance;
void setup() {
  pinMode(trigPin, OUTPUT); // Sets the trigPin as an Output
  pinMode(echoPin, INPUT); // Sets the echoPin as an Input
  Serial.begin(9600); // Starts the serial communication
}
void loop() {
  // Clears the trigPin
  digitalWrite(trigPin, LOW);
  delayMicroseconds(2);
  // Sets the trigPin on HIGH state for 10 micro seconds
  digitalWrite(trigPin, HIGH);
  delayMicroseconds(10);
  digitalWrite(trigPin, LOW);
  // Reads the echoPin, returns the sound wave travel time in microseconds
  duration = pulseIn(echoPin, HIGH);
  // Calculating the distance
  distance = duration * 0.034 / 2;
  // Prints the distance on the Serial Monitor
  Serial.print("Distance: ");
  Serial.println(distance);
}
First, it will read the values from the serial monitor. Then, I would like the HC-05 module to take these numbers and continuously send it to my Android app, which will then process what to do with the numbers.


No. What you do is you connect your Bluetooth module to two digital pins, which you'll use, along with the SoftwareSerial library, just the way you are using currently the Serial object. Look at the SoftwareSerial examples in the IDE.

Before you use the HC-05 module, and transmit data, you'll have to make sure it is set up properly (baud rate, name, PIN code, etc). Plenty of code and tutorials on Google about that.