Bridge saddles almost all the way up.

I would take the neck off and see if there's a shim underneath there.

 

How's the relief?
If good, you can shim at the front of the pocket if necessary...

 

If it's a brand new bass I'd return and exchange it as that sounds like there's a problem. I've owned lots and lots and lots of basses, and never encountered that. I've had the opposite, where the saddles were flat against the bridge, but having them all the way up could and I think will cause problems somewhere down the line.

Do you know how to sight a neck? Is there an incredible amount of back bow? Have you loosened the truss rod at all and did it make any difference?

Also, what kind of bass is it?

 

Don't just got adjusting the truss rod willy nilly. Learn how to check the neck relief & adjust accordingly.

 

Probably a daft question, but I assume we are talking standard tuning?

 

Do you hit your strings hard? I could get TIs on a P to have really low action usually (but I play with a very soft touch), so I'm asking.

 

You can always put a shim in the back part of the neck pocket (opposite of what people normally do with shimming). That will angle the neck downward slightly, and you'll have more height on your bridge saddles.

 

I have TI's on 2 basses you need to lighten your playing style. I had to adjust how I play. A lot of guys can't play TI's because they are loose feeling. Labella low Tension Flats are a good alternative to TI's. A little more tension and great tone.

 

If you had the neck off are you sure you got it seated properly when you put it back together? The screws should slide through the body without resistance, if they don't they can cause the neck to seat improperly, leaving gaps and an elevated neck that may or may not be crooked in the pocket.