Agree with Tim about the raw cider vinegar bottle. I don't normally go out of my way to overly sanitize, but make sure you clean it out well and that there is no residual smell from the vinegar. Even if your mead doesn't turn to vinegar, you may be imparting some unpleasant flavors. Regardless, if it's a glass jar and you clean it well, you should be fine.
Your technique sounds fine. That is the most basic technique and you will almost definitely come out with mead in the end. The one caveat about brewing honey-water with no additions is that you increase the likelihood of some off flavors. Don't let that stop you, but I will sometimes add whatever fruit is on hand or some spices (cinnamon, cloves, ginger, etc.) for flavoring and to speed up fermentation. I almost always add organic raisins, as they are usually covered with wild yeast. Also, another tip I recently picked up is to prepare a ginger starter about a week before you're planning your first batch. This is a good method for naturally inducing fermentation. Simply chop some ginger and add it to about two cups of water and half a cup of sugar. Set it somewhere warm covered with a cheesecloth, stir regularly, and once it starts fermenting, add it to your must (un-fermented mead).
If you're looking for a step by step that avoids all the over complexity you'll find in most mead recipes, I've written a few blogs. This is a good one for starting out:
http://www.earthineer.com/content.php?blogid=20656 I apologize for the odd font sizing. The site is currently in beta, but a major revamp will be coming out soon. Also, I've outlined a method very similar to what you're describing in the current copy of New Pioneer Magazine. Good luck!