It would help if you could tell us what "the dot" are? Do they bite, or do they just nip (which is a small, relatively painless, bite)?
But I see in the second half of your sentence that "the dot" is suddenly singular. What is it?? Shouldn't it be "...tries to bite/nip...."?
Ah-ha!! Trisia, you may well be right.
Then it depends on whether the dog is an alsatian or a toy dog that looks more like a rat on a string. They try to bite, but what results is normally just a nip. And a dog doesn't necessarily need to be agressive to bite or nip. Just being friendly suffices sometimes.
And I'm not sure that the use of bite and bit in the same sentence is all that horrific. I would use bite (in deference to the rat's feelings).