He didn't go alone...he went with Marsellus but Marsellus left to get coffee while they waited.
Meanwhile Butch has since betrayed Marsellus, who vows to kill him. While Marsellus and Vincent are staking out Butch's apartment, Marsellus leaves to get them some coffee and Vincent goes into the bathroom. Butch warily walks in to retrieve a forgotten watch and finds a Silenced MAC-11 on the kitchen counter. As he picks it up, Butch hears the toilet flush in the bathroom. Vincent walks out and freezes, recognizing Butch and staring into the barrel of his boss' gun.
When Butch leaves he sees Marsellus coming back from getting the coffee...
Certainly you could argue that they should not have split up but stakeouts (at least in movies) often involve one person being alone for a short time.
There is a common theme of bad things happening while Vincent is the bathroom
While Vincent is in the bathroom, Mia finds his heroin, mistakes it for cocaine, snorts it and overdoses.
While Vincent is in the bathroom, a couple, Pumpkin and Honey Bunny, hold up the restaurant.
While Vincent is in the bathroom and Marsellus is out getting coffee, Butch returns and grabs a gun.