To think this wasn't the best way to handle the situation

[Alisvolatpropiis]

I was on the bus earlier on and a lady got on with a medium size dog (not a guide dog), this is perfectly acceptable where I live.

She sat on a fold down seat at the front of the bus (the pushchair and wheelchair area). The woman sitting next to her (on the normal seats), so facing her rather than next to her iyswim? This lady had her daughter with her,she was under 5 (I think).

Anyway the little girl practically backflips on to my lap in her effort to get away from the dog. Repeatedly. She is obviously very frightened. Mum is obviously used to this and doesn't make a fuss,just goes about calming her down.

The woman with the dog says to the little girl "don't worry I won't let him bite you". Why on earth would you say that to anyone never mind an obviously frightened child?

There was nowhere for the mum and daughter to move not the woman and dog. So it couldn't be helped. But the woman kept going on and on about how she wouldn't let her dog bite the little girl.

I have a dog, I like them. But I just thought what the woman was saying was ridiculously stupid. The dog was a placid old thing. She could have said "don't worry,he'll just sit quietly, he won't come close to you,I can see you don't like dogs".

I honestly wanted to bash my head about the window.

Surely saying, 'he doesn't bite' would be better? Rather than admitting that the dog does bite?

I hate it when owners say, 'he won't bite, but he might lick you to death..'! The thought of a dog licking me makes me gag.

I don't doubt she meant well but I just kept thinking "please god stop saying bite woman!".

I highly doubt the dog had ever bitten anyone in his life. It seemed such an unnecessary/thoughtless thing to say once never mind repeatedly!

The mum should have said something of she had a problem. The dog owner was just trying to reassure a nervous child.

My neighbour has a over eager dog that yaps at children when on the lead and she always, repeatedly says "he lurves small children but he can't manage a whole one hahaha" Oh it drives me mad as DC will ask what does it mean and go on about the dog eating them.

It sound like it was a well-intentioned attempt to reassure the girl, but the choice of words made it less helpful than it could have been. Apart from anything, being bitten isn't always the root of the fear with dogs, so it might not have been helpful anyway.
Reading your OP though, I think the mother should have stepped in - she must have had more of an idea of what the girl was actually scared of, so in her position I would have said something reassuring to add to what the owner was saying e.g 'See, you don't have to worry about getting bitten, or licked/jumped on/pushed over'. It's a shame she didn't join in, or even say to the dog's owner 'She's mostly worried about x,y or z, but your dog won't do that will he?'. Poorer choice on the mother's part I think...