When breech seating bullets, how much of a gap is there between the bullet base and the wad covering the powder? I know in BPCR, I have been told to never leave an air gap.

............. that's not what I've read. Ringing a barrel with a gap is possible with older barrels due to their softer steel, regardless of the barrel thickness. Modern steels are considerably stronger and do not suffer the problem. But, I would not leave an air gap in my all original 1897 High Wall or Hepburn. Better to be safe.

So far, all posts are correct, as far as they go. A bit more detail makes it all clear. 
If you dig way back, c. 1900 era, a card wad was used in the case mouth to hold the black powder or duplex load in place and whether breech seated or muzzle loaded, the bullet base was approximately 1/16" ahead of the case mouth. Barrels back then were definitely soft steel.
If you are talking air gap between wad and smokeless powder, then Charlie Dell's research about ringing a chamber is relevant.
If I were to throw out a question, it would be; why would you use a wad with smokeless powder?
Happy new year and good shooting to all in 2015!

I use a tuft of Dacron filler above 4759 in my 38-55 ... but I would NEVER equate to being a 'wad'. 

There are indeed wads and fillers ... just never confuse the 2!

I would shy away from using Dacron it melts into a Goo and is well known and noted for destroying barrels. Do as you please but you might be better served to use a tuft of Kapok in its place.

The air thing with BP is one of the inthernet myths that got started somehow, and  kept going on  to become an absolute it never was - it didn't exist in the day, even a noted maker like W. W. Greener advocated the use of partial loads if the correct (BP) granulation was not available.
If max. accuracy is your game, you will be better served with loads without an air gap, true - but any reasonable BP load with air between powder and bullet (but don't seat the OP wad on top of the powder) will NOT harm the rifle, even with original soft steel barrels.  It mightn't be the most accurate load, but that's another thing.
How do I know? From shooting 1000+ BP rounds in original rifles (Mainly Martini's in 577-450 and no.2 Musket), and yes, they are all as good as ever, no chamber ringing, no bulges.
If you completely fill a 577-450 case with powder, you're arriving at around 110+grs of powder behind a 500+grs bulletis a military rifle - that hurts!

And going to the smaller black powder cartridges, Stevens (in their Catalog No. 50 on page 98)
describes reduced loads for their 22-15-60 cartridge as follows:
"By reference to the cuts of bullets for this cartridge, it will be seen that it can be loaded, .22-3-32, .22-5-40, .22-7-46, .22-10-46, .22-13-46.  Use a soft lead bullet, seated in usual manner in mouth of shell and a thin wad over powder.  Grain of powder will vary with the rifle, but the smaller loads will require a FFFFg or FFFg, while the two larger will probably do best work with the FFg size.  ..."

The "reference to the cuts of bullets" are for the various weights available for the Ideal bullet mould numbers 22636 and 22637.

There is a product out there called Puf-lon.  It is not a wad, but a filler material maybe graphite/molydenum mix?  It is loaded on top of the powder so that there is no air gap.  Anybody have any experience with this stuff in either smokeless or black powder?