Elinchrom BXRI 500 and HSS

Can I use sync speeds faster than 1/250 with the bx-ri 500? If so, how?

Why would you want to?

To control ambient light

First; HSS is a proprietary technology camera manufacturers employ to permit their speedlites to pulse a continuous light while the shutter curtain slit travels across the sensor.

What you are probably asking about is what PocketWizard calls Hyper Sync. This is a hack that fires the studio strobe early so that the "big" flash occurs before the first curtain clears the sensor, this permits the tail that occurs after the "big" flash to light the subject while the shutter slit travels across the sensor. Because the tail is a continuously weaking light source there will be a gradient from the starting "side" to the finish.

Ironically, most monolights, have a longer tail (flash duration) as power is reduced from full power. So, more powerful light at lower power setting will work better.

Controlling ambient light can be accomplished with the aperture.
If you want to maintain a shallow DOF, then neutral density filters can be employed.

As David points out, it can be difficult to achieve consistent flash exposure across the frame with hypersync.

Got it. Thanks guys!