How do I make the HC-05 bluetooth module take data from the HC-SRO4, and then send it to my Android app?
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.