I'd say the risk of killing someone or causing an incident is much lower when riding drunk on a bike than in a car. To cause a major accident while drunk on a bike (that doesn't only involve yourself) you need an unfortunate chain of events such as a car avoiding you and running into someone else.
For starters, I can usually go most places by bike without doing it on the same roads as cars. (I know that's rarely the case in the US though). If that's not possible, and you are so drunk you can't ride a bike (I can certainly ride a bike safer than a car while drunk simply because the speed is much slower so the reaction times are longer) - then leave the bike too. Walk or get a cab.
College years have provided me with both first and second person anecdotal evidence that cycling can have a higher incapability threshold than walking. That's for the motor control parts at least.
Situational awareness is an entirely different story though. In the dead of night traffic is on easy mode, where you notice the indirect illumination of a car's headlights around two corners and hear them from a mile away. That's just not very challenging (and probably plays a large role in the seemingly universal pattern of more drunk driving in rural areas, unfortunately cars come with an incredible amount of risk compensation through speed). Broad daylight city cycling on the other hand I consider a bad idea even at BAC levels well within the legal limits for driving cars (speaking of Germany here, where in terms of fines, cycling is tolerated at twice the BAC level as driving, a reasonable compromise)
Except when you're driving at night without lights and are too buzzed to pay attention to traffic.
Road traffic relies on cooperation between the participants. If you can't pull your own weight (i.e. follow traffic laws, control your vehicle, etc), you don't belong on the road.
Also it's not about yourself. Sure, if you kill yourself in an accident on a bicycle you're less likely to injure somebody else but you're still inflicting all kinds of harm on others.
