Suppose you distribute via a .zip file
You can delete a copy of the JRE in your application directory, and then create a .bat and .sh script that will launch the application using the java command using the JRE located in the same directory.
This may be the best tool for this, but it is one of the ways this can be achieved.
Super simplified .sh script example
#!/bin/bash
jre/bin/java myapp.jar
myapp.jar, JRE . , , JRE .
:
myapp/
jre/
start.sh
start.bat
myapp.jar
jre JRE.