How much more does an autoclave help with bridging compared to just vacuum bagging? Any? How about air bubbles?
Short answer:
Alot. Gone.
Longer answer:
With vacuum you can only get 1 bar (10 200kg/m2) of pressure pushing any one spot, with an autoclave you can get 4 bar (40 800kg/m2) or more. However you still do need to watch for bridging just not as badly as long as the bag doesn’t bridge too. For example we made some parts in prepreg which had been infused, there was an area that they could never get to form up and just ended up resin rich and in the bin. Using prepreg and the autoclave we nailed it first go.
Air bubbles, as long as there is no leaks, will not occur. We run vacuum on the part as well as the pressure so any air is squeezed/sucked out. The resin get “hydrauliced” to the surface displacing any bubbles. The pressure also dissolves any air into the resin, like any of your favourite carbonated beverages before you open them.
How do keep a vacuum on your part inside an autoclave that is sealed? Does the pump go inside or are the tubes that run outside of the autoclave or is a perfect seal needed to maintain the vacuum once it is pulled?
Here is a picture of our autoclave. The vacuum lines can be seen on the inside along the side coiled up. They are screwed into side of the autoclave and on the outside you can see 7 taps (there are 8per side) which attach to the vacuum. The taps allow us to isolate unused lines and there are quick release fittings above the taps to allow us to check for leaks. (if there is a leak it blows air out the line)

That’s not making much sense to me…
CO2 (0.033% of air’s content) dissolves better as pressure increases and temperature decreases, this is how beverages can be carbonated.
Nitrogen (78% of air’s content) hardly dissolves at all - it’s nearly insoluble.
How would air dissolve when it’s largest component isn’t taken to dissolving? At elevated autoclave temperatures, no less?
I personally have never heard that. Any gas in a liquid, means a bubble. A void in resin, big or small. Fine, you compressed the bubble to 1/10th of the size, but then you have a bubble that is holding pressurized gas, waiting to be let out. Autoclaves use vacuum and pressure to put out any entrapped air. There has to be an air flow out of the bag, be it breather, or whatever.
As for bridging, you have to bag even more carefully because instead of 14psi, you have 100-300psi pushing onto that bag that is stretching. It will break!
However, if you are using a nice elongation bag, and you suck at bagging, yes, the more pressure will eventually push out the bridging. Still not a good idea to suck at bagging 
Canyon: The hoses are connected by feedthroughs through the wall of the clave. Some use QC’s some use screw on fittings. On most occasions for epoxy and thermoplastic prepreg, you vacuum the part down, add pressure, and then vent the bag to atmosphere (outside, obviously). So the bag is seeing the 100-300psi pushing on the bag, but the bag internals are “open”
to the outside world. There is debate on WHY you vent, vs. keeping the vacuum pump on, but I never understood them. I’ve heard that it is a grandfathered process because back in the days, prepreg was NOT net-resin, and you didn’t want resin to be sucked into your vacuum pump.
There are plenty of examples of gasses dissolved in liquids without bubbles: acetylene is dissolved in acetone, air in sea water, nitrogen in a divers blood which if pressure is released too quick causes decompression sickness. At 1atm you can dissolve 0.023g/kg of air in water, at 4atm you can get 0.091g/kg.
air dissolves, look at fish
N2 does dissolve quite a bit, divers will know this well because it can kill you. to my knowledge N2 and most all other gasses will freely dissolve in water, now lets consider that we are talking about disolving those same gasses into resins which are do not often share many physical or chemical proterties similar to water. my educated guess would be that this is simply compressing the bubble to a smaller size and not actually disolving it…