If you're doing it properly, you should be making the tea in a pot first, pouring the milk into the cup or mug, then pouring the tea from the pot into the cup once it's brewed.
I'm quite lazy at work and pour hot water directly onto a teabag in the mug, wait about half a minute for it to brew, remove the teabag then add the milk. Milk + teabag doesn't go together well, IMO.
You can buy two sorts of teabags in the UK: regular and 'one cup'. The difference is basically that 'regular' is stronger, and tends to be a blend of teas. Since 'one cup' teabags are nearly as, if not more, expensive compared to regular ones, a lot of people simply use regular bags for making single cups and whip the bag out sooner.