Can someone recommend an inexpensive and reliable lens for shooting birds?
This is almost like asking for a recommendation for a lens for photographing people. A good lens choice will depend on your approach skills, the size/kind of birds, the kind of photos you wish to make, and of course your budget for a lens.
For example: are you interested in documenting rarities? BIF? nesting behavior? fine art (i.e., well-composed, rich color, exceptional detail) photos? How good are you at getting close to birds? Are you interested in tiny passerines, herons in Florida, hawks at a migration point? What sort of habitats are you likely to encounter? Dense brush, deep forests, open plains? The answers to all these questions (and more) will point toward a variety of lenses. I typically use lenses from 280mm to 560mm. Much of the time the 280mm lens is on the short side of usable but in other situations it's just the right thing; the 560mm lens is manual-focus, relatively slow, relatively affordable, very portable and perhaps my most productive lens.