You should leave the bottles open and covered with muslin until there are absolutely no bubbles rising in the mead. That could take up to 6 months, and sometimes my mead gets drunk before it gets that old! Once it stops bubbling it should be safe to put lids on the bottles and you can age it for up to a few years if you want. Apparently it gets better with age, but I’ve never had any long enough to find out.
Mead is a simple brew, and if you leave out the hops and make plain mead, it’s even simpler. In that case, there’d be no need to heat the water. You’d just stir in the honey and let it ferment.
Starting wild mead from scratch
Wild mead is a bit like sourdough. If you have wild mead already or can get some you like from a friend, you can use a bit of that to kick start fermentation. The yeast and bacteria in the mead will stay healthy as long as you keep taking a little of your last batch and putting it in a fresh batch. Because wild fermentation happens naturally and is based on a whole ecosystem of yeast and bacteria, the balance of organisms is far more resistant to contamination than single-species brewing yeast and once you have a healthy mead, you can keep propagating it almost indefinitely.
If you start mead from scratch, you need to put a bit more effort in to create an environment that will encourage the microorganisms that you want to grow, and discourage the ones that you don’t. You need to stir or shake the bottles at least once every day until you can see constant bubbling, and it helps to put an antibacterial herb such as hops or rosemary in the bottles. You also need to mix in at least some cold pressed honey, because this contains dormant yeast and bacteria perfectly suited to ferment honey. Once you dilute the honey with water, they’ll wake up and start to do their job.
The amazing book The Art of Fermentation by Sandor Ellix Katz has a lot more info on the infinite variations of this deceptively simple brew.