Yes, the pressure will be 3ATA no matter what the size of the bubble is, assuming a rigid container. Look at it this way: water is incompressible (well, neglegibly so under these sorts of pressures). So instead of a 1000ml container with 100ml of air and 900ml of water you can just imagine that the 900ml of water is "transmuted" into glass, leaving the container filled completely with air at 3ATA. And if the container is sealed after putting the air in, the pressure inside is constant from that point on, regardless of depth.
Substitute 1ml or 999ml for the air volume and the reasoning (and results) are the same.