While building a bed frame, at what point should I start worring about cross beams?
Lateral support is probably very important. Over time your bolts will not grip as strongly, and the legs will start to wiggle. Bracing the legs to each other or to the top of the bed will counter this rotational tendency. You'll need to fasten each leg at two points to make this work right, so you might consider the following options for securing each leg to the adjacent legs:


Strapping a wide (probably 6+ inches) board across two legs, fastening at the four corners, or
Trusses, fasten the bottom of the left leg and the bottom of the right leg to the same point on the lintel, or
an X shape between each pair of legs, with a fastener in the center.


As this is a bed and will be subject to... ahem... use, you'll probably want some sort of bracing.