In reply to boseow25: A separate bivvy bag and s/bag is the only way to go: warmer, and more flexible (you can use the s/bag alone in bothies or indoors, and you can use the b/bag in summer with a thinner s/bag).
Choice of bivvy bag basically boils down to a simple sack (look out for a decent hood) or a hooped bivvy. The latter is likely to be more expensive and heavier, indeed in my opinion you might as well have a lightweight tent as the they don't weigh that much more and are a much less claustrophobic living experience. I would go for a simple non-hooped bag.
As for the s/bag... For best warmth-to-weight down is the way to go. It's more expensive but lasts longer. The disadvantage with down comes in damp conditions, but if it's not sub-zero and dry outside then I for one would not aim to be bivvying in winter anyway. If you pick your nights with that in mind, and don't aim to be out for extended periods of time (over several nights a down bag will probably get damp) then the damp/down thing needn't be an issue. I wouldn't spend more on a waterproof bag (if such a thing exists?); the outers of decent down bags will repel a reasonable amount of moisture anyway, and you don't need anything (a membrane, say) making it less than optimally breathable. That's what a bivvy bag is for.
Lastly I'd echo what the first poster said: if you're looking to get early starts on the crags and achieve plenty of climbing then bivvying is usually a mug's game. It's more faffy and more arduous than sleeping in the glen, and by the time you've brewed up and thawed out your fingers you could easily have walked in from a nice warm valley base.
However, if you're looking to get away from it all and treat the night out as part of the fun, and not necessarily needing to perform to your best the next day on the climb (say you're off doing easy routes somewhere remote) then bivvying has plenty to recommend it. But do pick your weather window with care, or it'll be misery at best.