Some good advice in this tutorial for making a close approach to a bird. Arash Hazeghi is a master bird photographer who knows what he is talking about. Read his tutorial here http://arihazeghiphotography.com/blog/how-to-get-close-to-your-subject/

A few things I do:
1. If possible, I try to move in the shadows, if there are any, in the hope it will make me less obvious.
2. A completely different approach for some species, especially small birds that I often find are more tolerant of people or at least don't sometimes notice us, is to watch behaviour and pick out a spot that they might visit. Stand still there for a while and you will sometimes be lucky with quite a close approach. I've sometimes waited 30 minutes or more. It also enables a shot to be set up more easily as you will have some choice about direction of light, background etc. It can produce unexpected results though. One time I tried it with a Scarlet Robin. I was patiently waiting and heard a sound close behind me. The bird (a female) had landed within touching distance and stayed for a short while - seemingly unperturbed - as I slowly turned to watch her. A beautiful experience but useless for photographs!