How to drill straight hole in 4x8 beam?
You could try clamping something rigid and relatively straight (like a T-square or 1x4) to the beam and then using that to ensure it's perpendicular. Then measure your holes and drill with, say, your knuckles making contact on the rigid surface

If I were you, I'd just buy a longer bit tho. Sounds like a waste, but when you need the right tool, you need the right tool. And it makes life easier. Your regular bit may not penetrate enough to connect the holes (I've had that one happen).