Bed

The "for" is unnatural to the native ear.

We're ready for bed.

We get ready for bed.

We may go home for the purpose of going to bed, but we don't say it that way.

"Going to bed" and "ready for bed" are fixed expressions.

but I've heard ppl use:

I went home early for bed. Is this incorrect then?

Or

I went home for bed.

Or

I went home to bed.

I've heard people say, "I headed for bed," but I've never heard a native speaker say "I went home for bed."

Maybe it's British.

'to'. I've never heard people use 'for'.

If the intended action is to go home to sleep, most native speakers would say "went home to bed".