Looking at each part of each card:

Draw ability both have variance in what is going to happen.  Bob's ability reveals the card, and does a lot more damage on average.  Bob is also limited to a maximum of 1 card per turn regardless of the situation, although that card is guaranteed.  In any deck where you go hellbent often, workshops/dredge/dragon/ect., this is way better than Bob.  Asylum Visitor has the bonus of potentially causing your opponent to take suboptimal lines in order to try and shut off the ability too.

P/T edge goes to Asylum Visit as 3/1 > 2/1.  This power difference is also not negligible as it can trade with Lodestone, kill Jace in one attack, trade with a blocking Mishra's Factory, and provide a clock that is 3 turns faster.

The Madness ability.  This is obviously something Bob doesn't have at all.  Asylum Visitor has already generated card advantage just by being cast off its madness ability, regardless of whether it resolves or is removed before it ever activates.

Honestly this card is of a higher power level than Bob although in some decks, Bob would likely be the better choice.

The only way I see this working is if you cheat on costs, which is why omniscience seems like the only deck this makes sense in to me, also because you can chain them In that list. Omniscience into 2 duress effect into another one of these into more duress, eventually into wincon or whatever.

But since Omnitell is really just a niche deck in vintage if at all, Not sure where this would fit. Maybe it would be nice to hit of minds desire or something?

I'm assuming by the time you cast this you have already cast a flurry of rituals (dark or cabal with threshold) and maybe a Gitaxian probe this knowing what they have and what to grab.

Assuming you cast this and still have at least 1 mana available for Flusterstorm, right? And even if you do, you may have to work with Lotus mana only after will. Also, in this case, Flusterstorm doesn't win a counter war against 2 counters.
And if you pass the turn to untap, Flusterstorm gets way worse.

While I applaud the design and power level of this guy, I'm not really sure what makes him any more suited to Vintage at the moment than Dark Confidant. Bob barely gets a look-in these days, and as long as mid-range gro decks (and the removal we all run because of them) continue to be a thing, I doubt this guy will either.

That said, if Gush ever gets restricted we might be back to looking for other draw engines. Still, even then, Bob seems far more reliable, especially at helping you hit your land drops versus Shops, so you can even begin to think about emptying your hand.

Cool card, but I'm not really seeing it in Vintage.

lotus, yawg will, flusterstorm doesn't get you there after what?

You can draw multiple cards if you happen to draw and use a counterspell/removal or any other instant on your opponent's turn that doesn't read draw a card. 

However, the biggest and best way to get multiple draws off this is Bazaar of Baghdad.  It's also how you abuse madness.  Another good card with both this card, and Bazaar?  Uba Mask.

This card is very powerful, but it's fairly cost.  It's so close.

Nice!

You guys could also link to the NorCal Old School rules: http://www.eudogames.com/magic/160228-old-school-magic

so multiple copies are great vs a hellbent opponent, but not good for you unless you can cast an instant in between resolutions.

The ability only triggers once each upkeep, so you can only draw 1 card per turn.  There are situations where you can draw a card on your turn and a card on your opponents turn.