A "fitness bike" like a Trek 7.2FX should work for you in both situations just fine and fall into your budget range. You should be able to fit it with either a rear rack/trunk bag/panniers or front handlebar bag/basket, or both to carry your birding stuff. Bags are usually removable, so you can pull them off and use either a smaller version or just a small saddle wedge when doing your fitness riding.
If you are used to road bikes, you might also consider a touring or cyclocross bike.
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"Let us hope our weapons are never needed --but do not forget what the common people knew when they demanded the Bill of Rights: An armed citizenry is the first defense, the best defense, and the final defense against tyranny. If guns are outlawed, only the government will have guns. Only the police, the secret police, the military, the hired servants of our rulers. Only the government -- and a few outlaws. I intend to be among the outlaws" - Edward Abbey