How to generate the same Bearer token as Swagger?

Don't be confused, this is using OAuth 2.0, and not basic authentication (which would be much easier to do yourself).

In SoapUI, you can set up OAuth by going to a request and clicking the Auth tab along the bottom, and Add New Authorization...

But you mention youre using your own app (and not SoapUI?). OAuth 2.0 is a slightly complex multiple step process - I think these days people are mostly just using a library to handle it.