I usually have my birth stuff sitting in a box ready to go from about 37 weeks or so. When contractions start, I give my midwife a call just to say hey, something's going on, but not sure if this is the real deal yet. When it gets "real" DH usually calls (generally I'm a little irrational at that point ) and says "COME NOW!" and it has worked out fine. The midwives have arrived in good time and were ready because they had the heads up earlier in the day.
We usually make the bed up with a plastic sheet over one set of sheets, and then an old sheet over top of that when labour is well established. I've delivered in the bath, but we use the bed for post partum checks, baby exam, etc., so when that's all done, we can take off the old sheet and the plastic sheet and have a clean bed ready to go underneath.