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Maybe it did cloud his mind a bit, so for a short time, he wasn't obsessed with it. But I wonder how long it was out of his possesion before Bilbo happened upon it.
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I don't think it could have been out of his possession for very long i.e. more than an hour or so. As
Legate points out, though Gollum no longer wore the Ring frequently, he still needed to check on it constantly.
This need to constantly check on his Precious leads me to think that the period of time between Gollum losing the Ring and Bilbo finding it must have been short indeed. In the same way that a Ringbearer can be fiddling with the Ring and not be immediately aware that he is doing so (e.g. Frodo at the Prancing Pony), I think that he can likewise lose the Ring and not immediately be aware that it's gone (perhaps due to some "clouding of the mind" caused by the Ring). Therefore at the time that he meets Bilbo, Gollum probably has not had sufficient time to register his loss and then he is distracted by his curiosity, wanting to find out what Bilbo is and then later by the Riddle Game.
As for why it doesn't immediately dawn on him after the Riddle Game that he has lost the Ring? I think this might be explained by : (a) he was upset at losing the Game which (b) caused him forget that he was supposed to have the Ring on him and instinctively head towards the island, the place where in recent times he is used to keeping it. I don't think that this "forgetting" is necessarily connected to the Ring but is similar to forgetting that my cell phone is in the laptop case and instinctively searching my handbag where it normally stays.