From Cache how to Retrieve and Use/Reuse a Bearer Token to authenticate and send data to REST web service?

For the first part of your question, here's a sample method that gets a bearer token from the request:

ClassMethod GetAccessTokenFromRequest(pRequest As %CSP.Request = {%request}) As %String
{
	Set accessToken=""
	Set authorizationHeader=pRequest.GetCgiEnv("HTTP_AUTHORIZATION")
	If $zcvt($piece(authorizationHeader," ",1),"U")="BEARER" {
		If $length(authorizationHeader," ")=2 {
			Set accessToken=$piece(authorizationHeader," ",2)
		}
	}
	return accessToken
}

EDIT: And here is a full sample of a REST handler that retrieves a bearer token and reuses it to make a request against another REST service.

Class API.DemoBearerToken Extends %CSP.REST
{

Parameter APIHOST = "localhost";

Parameter APIPORT = 52773;

Parameter APIPATH = "/some/other/path";

XData UrlMap [ XMLNamespace = "http://www.intersystems.com/urlmap" ]
{
<Routes>
<Route Url="/example" Method="GET" Call="example"/>
</Routes>
}

ClassMethod example()
{
	set accessToken = ..GetAccessTokenFromRequest(%request)
	set req = ##class(%Net.HttpRequest).%New()
	set req.Https = 1
	set req.SSLConfiguration = "some ssl config"
	set req.Server = ..#APIHOST
	set req.Port = ..#APIPORT
	set req.Authorization = "Bearer "_accessToken
	$$$ThrowOnError(req.Get(..#APIPATH))
	set %response.Status = req.HttpResponse.StatusCode
	set %response.ContentType = req.HttpResponse.ContentType
	if req.HttpResponse.StatusCode <= 400 { //if not an error response
		set jsonData = {}.%FromJSON(req.HttpResponse.Data)
		write jsonData.%ToJSON()
	}
	return $$$OK
}

ClassMethod GetAccessTokenFromRequest(pRequest As %CSP.Request = {%request}) As %String
{
	Set accessToken=""
	Set authorizationHeader=pRequest.GetCgiEnv("HTTP_AUTHORIZATION")
	If $zcvt($piece(authorizationHeader," ",1),"U")="BEARER" {
		If $length(authorizationHeader," ")=2 {
			Set accessToken=$piece(authorizationHeader," ",2)
		}
	}
	return accessToken
}

}