You can bath him whenever is convenient at this age. I wouldn't worry too much.
At 4 weeks old baby should basically just be sleeping all of the time - day and night. You should be looking at wake, feed, nappy check, maybe 10-15 minutes happy/awake time through the daytime then offer a feed again to make sure full, wind and back to sleep.
So really you've only got 30-45 minutes awake during which you feed, check nappy, wind, little cuddle and that's it. Do this is a lit room. The only difference at night is less cuddle time, so maybe only 20-30 minutes awake for a feed, wind and nappy check, and it's done in a darkened room.
Is your baby waking for long periods of time in the night or waking frequently but going back to sleep easily?
By bedtime routine, I assume you mean things like bath, sleepsuit on, story maybe signalling bedtime. It's fine to do that now, just it will be flexible. Baby is unlikely to be 'going up to bed' for several months yet. But you can still start a routine.
Whatever time baby wakes up between 6pm and 8pm, call that 'bedtime' and do your routine of changing clothes etc. But baby will need to stay downstairs with you until you go to bed. He may well have another 'nap' or two before you take him up to bed rather than staying asleep.