The best open source alternative to Bomgar is DWService, which is both free and Open Source. If that doesn't suit you, our users have ranked more than 50 alternatives to Bomgar and five of them is open source so hopefully you can find a suitable replacement. Other interesting open source alternatives to Bomgar are Remotely (Free, Open Source), Aspia (Free, Open Source), Rustdesk (Free, Open Source) and screensy (Free, Open Source).
DWService is an open source project which offers a service that allows access to remote systems (Windows, Mac, Linux, Raspberry...) using a standard web browser - without any component required on the client side.
The best open source remote desktop software. It is an alternative of TeamViewer and AnyDesk, but open source. You have full control of your data, no concern of security. You can use my rendezvous/relay server, or set up your own, or write your own rendezvous/relay server.