As I read your question, I have tried without success to search on the Internet how Bearer tokens are encrypted or signed. I guess bearer tokens are not hashed (maybe partially, but not completely) because in that case, it will not be possible to decrypt it and retrieve users properties from it.
But your question seems to be trying to find answers on Bearer token functionality:
Suppose I am implementing an authorization provider, can I supply any kind of string for the bearer token? Can it be a random string? Does it has to be a base64 encoding of some attributes? Should it be hashed?
So, I'll try to explain how Bearer tokens and Refresh tokens work:
When user requests to the server for a token sending user and password through SSL, the server returns two things: an Access token and a Refresh token.
An Access token is a Bearer token that you will have to add in all request headers to be authenticated as a concrete user.
Authorization: Bearer <access_token>
An Access token is an encrypted string with all User properties, Claims and Roles that you wish. (You can check that the size of a token increases if you add more roles or claims). Once the Resource Server receives an access token, it will be able to decrypt it and read these user properties. This way, the user will be validated and granted along with all the application.
Access tokens have a short expiration (ie. 30 minutes). If access tokens had a long expiration it would be a problem, because theoretically there is no possibility to revoke it. So imagine a user with a role="Admin" that changes to "User". If a user keeps the old token with role="Admin" he will be able to access till the token expiration with Admin rights. That's why access tokens have a short expiration.
But, one issue comes in mind. If an access token has short expiration, we have to send every short period the user and password. Is this secure? No, it isn't. We should avoid it. That's when Refresh tokens appear to solve this problem.
Refresh tokens are stored in DB and will have long expiration (example: 1 month).
A user can get a new Access token (when it expires, every 30 minutes for example) using a refresh token, that the user had received in the first request for a token. When an access token expires, the client must send a refresh token. If this refresh token exists in DB, the server will return to the client a new access token and another refresh token (and will replace the old refresh token by the new one).
In case a user Access token has been compromised, the refresh token of that user must be deleted from DB. This way the token will be valid only till the access token expires because when the hacker tries to get a new access token sending the refresh token, this action will be denied.