11:29 a.m. on June 16, 2009 (EDT)
First thing about bivuoacing is that it is just that - a bivuoac, an emergency camp, intended for a very short stop. It is something you do when you are caught out without full camping gear, either by choice or in an emergency. A bivy is not intended to be a comfortable rest and is often in a location where you normally would not stop. As such, you may be on the cold side and scrunched into an uncomfortable position. In any case, you do not have all the amenities of a standard backpacking, climbing, or backcountry skiing camp in terms of gear, location, choice and preparation of campsite, cooking and eating facilities and gear, etc.
That said, there is a school of thought, related to ultralight backpacking, that goes even beyond the ultralight practice, carrying nothing in the lines of camping gear except a bivy sack, the clothes on your back (maybe plus some layers, maybe with a down jacket, maybe with an elephant's foot), a small amount of food, and maybe a small stove to heat some water for tea. You travel until you run out of daylight and/or energy, haul out the bivy sack, climb inside, sit down or lay down where you are (maybe using your pack for a bit of insulation from the ice), tie into a belay anchor (depending on the terrain), nibble on your gorp, try to catch a few winks, then start moving as soon as it gets light. You do not change into your 'jammies. You sleep in all your clothes. Your gear stays outside (no room in the bivy sack), in the weather (many bivies are in storm conditions, due to being overtime and caught out), possibly also tied into the same anchor as you are. That is, except for your boots. You may or may not take your boots off, but you keep them inside the bivy with you so they don't get buried in the snow drifts or fall off the ledge (but be aware that you might have a hard time getting them back on in the morning). Been there, done that.
Then there are the would-be ultralighters who decide this is the lightest way to go. These folk usually add a siltarp, maybe a full cooking outfit, and a fancy sleeping outfit (a full sleeping bag and a sleeping pad). They even take a pack cover or a plastic garbage bag to protect their gear (hey, the gear was made for the outdoors. It better be able to take a bit of snow and rain). Thing is, if you are going to take the sleeping bag and pad, you might as well carry a full tarp and dispense with the bivy sack (yeah, the bivy will protect the bag from the dirt or snow, but a small tarp or plastic sheet is lighter and protects the bag just as well under the tarp, and you end up with less weight).
Your questions -
Do you buy a higher temp sleeping bag cuz the bivy adds warmth?
If you are using only the bivy to sleep in, it is the same as a tent, so the bag is the same rating as if you were sleeping in a tent. But keep in mind that the material of the bivuoac sack is waterproof and nominally breathable (Goretex or some other wpb, usually, though some bivies are make of silcoat or other non-breathable material). It isn't really very breathable, so you can get condensation on the inside of the sack material.
How do you breathe if it is raining and you need to close it?
If you close up all zippers and velcro, you die in about 1-2 hours by suffocation. Well, no. Some bivies (Integral Designs makes the best) have a wire or plastic rod and mesh so you can have the face area open while shielded from rain and snow. Besides, you often bivy sitting up on a ledge or leaning against a rock or tree, so unless it is blowing rain or snow (common in a real bivy situation), you will not get any more water through the face opening than with your outer rain shell.
Where do you store your gear?
On the ground, snow, ice, ledge, next to you and within easy reach. Keep everything in your pack unless actually using it so it won't accidentally get kicked off the ledge. If there is any danger of that, you should anchor the pack (and yourself).
Bivy sacks are for bivuoacing. They are not tents. You want room for the gear? Get a tent. A good bivy sack is about 2 pounds (except for the ultralight emergency bivies, such as the one Integral Designs makes). You can get high quality small 1-person tents that have room for putting your pack inside at 3-4 pounds (Black Diamond's silcoat version of the Megamid is 1.5 pounds, plus use an adjustable hiking pole or tie to a branch to pitch it - even the non-silcoat version is 3 pounds and each will sleep 4 people). Or you can get a siltarp that weighs 2 pounds or less that is sufficient for 1 person. So there is only a tiny weight saving, if any, with a bivy sack.
Some people use a bivy sack inside a tent in the belief that it will keep them warmer. Aside from the condensation problem, the increase in warmth is no more than 5 degrees. If you have a leaky tent, it might keep the sleeping bag dryer.
pros and cons of each
Tents, hammocks, tarps, and bivy sacks are for different purposes.