@Panagrellus - As someone who plays bullet frequently, method 1 is definitely faster. It's one mousebutton press (hold, release) whereas method 2 you'd have to click twice.
I invested in a decent mouse (currently using logitech g300s, ~€35) and honestly it makes me win a lot of time scrambles. Definitely worth considering.
@Jayadeva - Bullet should be approached with caution, as it sharpens your intuitional play in manners you might not have thought of. You might get accostumed to playing a bad opening, for example, simply because it is easy to premove, or go for cheap tricks that are objectively speaking not good. If you're serious about improving your chess, avoid bullet until you have reached a certain level (e.g., once you have a solid opening repertoire, you will not get tempted into playing your bullet openings in longer time controls).
Bullet is not a good way to improve your chess, but it is a lot of fun (obviously).