How can I get a message bundle string from inside a managed bean?

There are two ways to get String resource bundle in managed bean, using baseName or varName (see definition of each one below):

Using varName:

varName: is the String representing the <var></var> in <resource-bundle>

FacesContext context = FacesContext.getCurrentInstance();
Application app = context.getApplication();
ResourceBundle bundle = app.getResourceBundle(context, varName);
String msg = bundle.getString("key");

Using baseName:

baseName: The fully qualified name of the resource bundle (<base-name> in <resource-bundle>).

FacesContext context = FacesContext.getCurrentInstance();
Locale locale = context .getViewRoot().getLocale();
ClassLoader loader = Thread.currentThread().getContextClassLoader();
ResourceBundle bundle = ResourceBundle.getBundle(baseName, locale, loader);
String msg = bundle.getString("key");

FacesContext context = FacesContext.getCurrentInstance();
ResourceBundle bundle = context.getApplication().getResourceBundle(context, "msg");
String message = bundle.getString("key");

here is key is property name which you want to access from properties file .

       message = This is "message"

This entry is from messages.properites file. and "message" is "key" .

You can get the full qualified bundle name of <message-bundle> by Application#getMessageBundle(). You can get the current locale by UIViewRoot#getLocale(). You can get a ResourceBundle out of a full qualified bundle name and the locale by ResourceBundle#getBundle().

So, summarized:

FacesContext facesContext = FacesContext.getCurrentInstance();
String messageBundleName = facesContext.getApplication().getMessageBundle();
Locale locale = facesContext.getViewRoot().getLocale();
ResourceBundle bundle = ResourceBundle.getBundle(messageBundleName, locale);
// ...

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Update: as per the mistake in the question, you actually want to get the bundle which is identified by the <base-name> of <resource-bundle>. This is unfortunately not directly available by a standard JSF API. You've either to hardcode the same base name in the code and substitute the messageBundleName in the above example with it, or to inject it as a managed property on <var> in a request scoped bean:

@ManagedProperty("#{msg}")
private ResourceBundle bundle; // +setter