This idea came to me when I was commenting on
nothingtosay's journal, and then she said that she'd also believed it for months! THIS MAKES IT CANON, and so I'm posting about it here. It all makes sense now.
Bob was a watchmaker, husband to a neurotic wife and father to a small, painfully shy child (he and Virginia despaired of where the eyebrows had come from). That is, until one day, he accidentally turned one of his timepieces to gold. He left his family and changed his name from Gray to Bishop almost immediately. After that, I'm not sure if Bob found the Linderman Group or if they found him, but in any case, it wasn't too long until he'd joined the Company and started rising in the ranks, due to the fact that he was a human money machine and just the kind of asshole they liked to put in charge.
Since Sylar is thirty if you go by the actor's age, and Elle is twenty-four, I'm giving Bob two years to have settled into Company life well enough to adopt the stray electric child that was passed into their care. That means that Gabriel was four when Bob abandoned the family - far too young to take over the watch shop. Bob could most definitely afford it, so he probably paid for the upkeep of the shop, and most likely gave Virginia some monetary help - not that he ever came home. This made Virginia angrier than anything, especially the fact that he preserved that damn watch shop for her special boy to take over when he was old enough. Imagine her fury when Gabriel did.
Bob kept tabs on Gabriel and Virginia over the years; not anything official and not anything noticeable, but he did. Just in case Gabriel had a power, obviously. He was disappointed when it looked like the only thing his son could do was fix watches reasonably well. Of course, Bob really sat up and took notice when Chandra Suresh arrived on Gabriel's doorstep with his book, and he found a way to inconspicuously bring it to the Company's attention - maybe through Bennet, who was already aware of Chandra and might not even have required prodding to start looking into his subjects. That's how the Company knew so much about Sylar's origins. They'd been watching him from the start.
Remember that phone call Bennet got when Sylar was captured? "There are no other options with an individual like this," he said, but he was ordered to keep Sylar alive anyway. That was Bob, who, for all his numerous failings as a parent, couldn't sign the order to execute his own kid (serial killer or not). Linderman, wrapped up in his plans for the future and Isaac's paintings and knowing Sylar had to play a part somehow, backed him up. And when Sylar escaped, that's why the might of the Company wasn't unleashed on his trail.
We know Bob was in NYC the night Peter exploded. Perhaps he was in the Kirby Plaza building, watching the events passing below. Or maybe he was already in the hospital with Elle, awaiting the arrival of Peter with his brother and Niki with her husband. In any case, he was the one who ordered Candice to get Sylar off the plaza, arranged the surgeries for him, and shipped him off to the jungle shack in Mexico when it was safe to transport him.
It's been asked over and over again why Sylar was kept in the middle of nowhere, in such a hovel, with only Candice to watch over him. Well, as the new head of the Company Bob might have had the resources and the authority to get Sylar taken care of, but establishing a link between him and his serial killer son would be a no-no on his part. Hence the secrecy.
Now, Bob was faced with a dilemma. He couldn't kill Sylar, but Sylar would not hesitate to kill him for leaving if they ever met face-to-face. The obvious solution was to take away his powers. Bob put a priority on experimentation with the virus, and they found what looked like a cure. They injected it into one of their prisoners, and for about two months (because one month is too short and three months is too long, given the four-month time frame) the subject couldn't use his ability, but was otherwise asymptomatic. Bob ordered that Sylar be infected with that strain... and not too long after he did so, the test subject became violently ill and died. And so Bob sought out and hired a certain Dr. Mohinder Suresh to find a cure for the virus - not because he was overly concerned with it becoming an epidemic (why would he have been experimenting with it, if that were the case?), but because he had a specific individual he needed to save.
And, again, this is why an alarm wasn't raised throughout the entire Company when Sylar escaped. Bob didn't want any of his agents finding and killing him in his vulnerable state. And yes, that's why Bob kept bringing Sylar up to Mohinder. He had a certain someone on his mind. :D
And yes, this means that Elle and Sylar are half-siblings. Apparently, all of Bob's children are psychotic killers. What a family.