A general rule that is not always fleshed out well in the language is that you should bond anything that is likely to be energized. If this fence is not near any energized conductors, it probably does not need to be bonded.
As an aside, it is probably fairly well "grounded" by the posts in the ground but that is not the same as bonded.
Places where I see fences bonded is where there is significant radiated power. This can be a radio/TV transmitter or just a big distribution transformer farm.
680 will also require that a fence be bonded if it is <5' from the water.
A friend bought an old farmhouse cheap, cheap because a new 400,000 volt line from a new atomic reactor passed close by [200 yards, heading for Italy]- and destroyed local realty values. Now the poco has bonded the neighbor's entire sheet metal barns and machinery shed. Is that why? Should he do the same to his barn, do you think?
I have a 250KV and two 48KV lines running behind my house and I can't seem to detect any strange voltage problems. I tried every YouTube trick I have seen to light a fluorescent tube with no joy. I even tried stringing 100' of THHN directly under the poles with various terminations or simply floating ... nothing.
It is a little disappointing actually. I thought I could get free lights for my boat house, virtually directly under the line.
