If you have an Android device you're in luck (for now)! Tweetdeck for Android currently supports hashtag alerts, although Twitter (who own Tweetdeck) has recently announced that Tweetdeck applications will stop working later on this year. Until that time, here's a video that shows you how to set everything up...
If you don't have an Android device there are less options. Firstly I'd recommend that you sign up to request Hashtag Alerts to be supported by Hootsuite... click just here.
Hootsuite say that this is currently under review so the more people who cast their vote the more likely it is to be included. Even if you've got an Android device I'd still recommend that you add the request to Hootsuite as it will give you an alternative method that you may actually prefer.
Another option is to set up your phone to receive an alert or text message every time @rbnUK tweets, here's how... https://support.twitter.com/articles/20169887-how-to-use-push-notifications
This will mean that you won't miss a thing. Although using this method means that you can't select which hashtags you're most interested in and you also won't receive alerts when somebody else uses the hashtag.
At Rare Bird Network we're constantly on the look out for ways to improve the service for you and enable you to receive free bird sightings information. If you know of any other methods please do get in touch.