Hello,
The difference between long lenses is rather less than the difference in wide lenses.
Most people would see the difference between a 28mm and a 24mm even though the difference in focal length of 4mm seems quite small, go down to 14mm (only 10mm further down) and the difference is huge in the picture.
On the other hand the difference between 200mm and 300mm is quite small in the image you get. Imagine your bird taken with the 200mm and its a small dot in the frame. Now imagine taking a third off the frame and enlarging the rest to fill the frame. Its a bigger dot but its not filling the frame! Thats the difference between 200 and 300mm only a third of the frame.
You either need to get very close with a normal tele lens (perhaps 10 meters) like a 300mm or find a really really long lens of 1200mm.
There is an alternative in the form of Digiscoping. Get a Terrestrial telescope and bolt a digital compact on the back. Theres a lot help on the web about this. The basic idea is that the telescope magnification is further magnified by the cameras lens (i.e. a 3X zoom lens on the camera = 60X on a 20X scope. 3X20). Its harder to equate this to a focal length and you may have to crop the image if you get a dark edging, which can be severe but it works well. Try searching Paul Hackett on the net, he is a leading exponent on the subject. Also contact
LCE in Winchester as they have a range of adapters to mount camera to scope (as well as scopes for that matter).
You are clearly keen an photography so you may well have a digi compact already, your budget would certainly get a half decent scope, try Opticron for good optics at good prices. The thing to look for is a big objective on the scope of 77mm+. The bigger the brighter.
Lastly use a really stable tripod!
Hope this helps
ilikebowens