Bilbo & Gollum

[lathspell]

I just did some checking in the Hobbit and the LotR and now I've got a question.

Gandalf tells in 'The Shadow of the Past' the history of Gollum. Gollum was a hobbit-kind of creature before he gained the One Ring.

'Long after the fall of Isildur, but still very long ago, there lived by the banks of the Great River on the edge of Wilderland a clever-handed and quiet-footed little people. I guess they were of hobbit-kind; akin to the fathers of the fathers of the Stoors...'

'There was a great deal in the background of their minds and memories that was very similar. They understood one another remarkably well, very much better than a hobbit would understand, say, a Dwarf, or an Orc, or even an Elf.'

So, most likely Gollum was of hobbit-kind. Bilbo of course is a hobbit... so my question is: why doesn't Gollum know what Bilbo when he sees him on the bank, and not even when he recalls memories of old times when he hadn't got the Ring yet?