Add "Toolbox" plugin to your Bubble application.
Add MUX Uploader element to your Bubble app and configure to match your setup. Refer to service page and demo editor for more details.
Set up MUX webhooks in your Bubble application to receive status upldates from MUX. Refer to the MUX documentation for detailed webhook setup instructions.
Demo editor:
https://bubble.io/page?type=page&name=mux-uploader&id=connectish-plugins&tab=tabs-1