From my tests on the PTR, it appears the way this ability works is, if you get more than one piercing shot effect within 8 sec, then the bleed ticks (which tic every 1 sec) will be temporarily increased. However, 8 sec after the first crit which started the piercing shot effect, the value of the tick will decrease, essentially taking it off the "stack", so to speak.
For example, if you get a chimera shot crit for 7k, then 2 sec later a steady shot crit for 4k, your piercing shot ticks will look like this (assuming no other crits, of course):
:01: 262
:02: 262
:03: 412
:04: 412
:05: 412
:06: 412
:07: 412
:08: 412
:09: 150
:10: 150