It doesn't look like anybody has responded to your post. I can't really help you because the only Air Venturi rifle I have is the original Avenger in .22 cal. It's a nice little rifle but I have mine sighted in for 50 yards and seldom shoot anything closer. I'm not a hunter, only target...
I'm no expert, but it seems the air is leaking out somewhere. If your pump is building pressure with a dead head but not on the rifle it has to be going into the the fill valve and tank or it would build pressure quickly just as it did with the dead head plugging off the hose.
Try a deadhead or plug in the air hose on your compressor. It might not be building pressure. It doesn't take much output to push air or bubble under water, but it takes a decent amount of pressure to open the one way valve to pressurize your air tube or tank on the gun.