Impossible to say for certain.
There is no tie-in material that covers Talia at all (she's mentioned by Garibaldi as part of his motives in Final Reckoning: The Fate of Bester, but that's it). So there is only TV series material to work from, and there are only two hints that Bester might know what is up with Talia beforehand.
Bester and his partner Kelsey run a deep scan on Talia in Mind War, probing to the point of pain, looking for any fingerprints that Ironheart had left in her mind. They don't find Ironheart's fingerprints, but they should and would have seen the fingerprints of her deep reprogramming and the sleeper personality. Even if they were not briefed on her mission and didn't know beforehand, they would have known that she had been altered at some point, and Bester would likely have followed up on this to the extent that he could.
Lyta does say in Divided Loyalties that the sleeper is designed to be invisible to a deep scan, so this may be ruled out. Still, if there is any point at which Bester should be tipped off, this is it.
- The episode A Race Through Dark Places
Talia enters Bester's mind and overwhelms it with a scenario that shows all the rogue blips dying, with help from all the other blips. On leaving the station, he hesitates, seemingly sensing that something if off but not quite certain what it is. Talia could block Bester's casual scans at this point (courtesy Ironheart), so he can't know what's going on her head right this moment, and it's likely he pauses because he knows she's been altered. However, it's possible he hesitates either because he knew about the sleeper and wanted to know what else was going on, or that the sleeper sent him a subtle communication at this point.
On the opposite side, there are several reasons and at least one piece of evidence to suggest he doesn't know at all...
- Deep cover agents are hardly advertised.
A sleeper agent like Talia, run by a shady operation so disconnected from the Psi Corps that they hide in old ruins (as shown in Spider in the Web), is only useful when very few people know about it. Such a mission would be on a need-to-know basis, and Bester didn't need to know - and we absolutely know that Psi Corps is fond of that reasoning, since Bester uses it the first episode we see him.
- Bester doesn't know everything.
Bester likes to act like he's the grand godfather of the Psi Corps, and in truth he's probably ranked high enough that he's not far wrong. Still, he doesn't run the place, and he clearly doesn't have insight into every branch of the Psi Corps as it starts to go in a direction he doesn't like. This is proven in Ship of Tears; he would not have come to B5 for help in countering his own people's shipment of blips to the Shadows if he had any other recourse, and even then he found he only had partial information on what was going on.
- The blips don't get caught.
This is evidence by absence, but... If Bester had known about Talia's sleeper, they would have communicated in A Race Through Dark Places. Following that, Bester or other Psi Cops should have been able to follow up on the not-actually-dead blips from the underground railroad and pick them up after they got off the station. We get shown later, starting in Grey 17 is Missing, that Franklin still has information on where those telepaths are and B5 begins recruiting heavily from their ranks, without any alarm that large numbers of them were rounded up.
So at minimum, we have evidence that Bester should have certainly known someone had worked over Talia's mind in the past, but little else, and several points weighing against him knowing the specifics.
Finally, JMS was asked about this idea, but was dismissive (without saying one way or another):
Did Bester try to befriend Talia because she was Control?
You're assuming Bester knows everything. Also, Bester's interest may have been more...carnal than PsiCorp oriented.
