I've noticed that Burst of Speed was frequently cooling down for me, and only getting a single extra use, so I started paying closer attention. Turns out what was going on was the 'counter' buffs that keep track of how many times you've used it were still hanging around after the cooldown finished, and I hopped on the test server to see what exactly was going on. What I found was Global recharge affects the power's cooldown, but does not affect these counters.
Burst of speed has a 1:30 recharge. When you use it once, you get a little buff to mark that. You use it again, and you get a second, again, and a third, then the power goes on and stays on cooldown. If you slot Burst of Speed for recharge, this 'counter' has it's length shortened to match with the cooldown of Burst of speed. If the cooldown is 1:17, the counter lasts 1:17. If the cooldown is 0:54, the counter lasts 0:54.
However, if you use something like hasten, or Reaction Time(From /Martial as well), the power itself will have reduced cool down, but those counters will be unaffected. Hence, Burst of speed could cool down in under a minute, due to global recharge bonuses, but keep the counters for 1:30. This results in getting one more use of Burst of Speed, ticking your counters up to 3+, and it goes on it's full cooldown again. This is true whether the Global Recharge boost is applied before or after Burst of Speed is used.
Note:
-In game, Burst of Speed has a small global damage bonus for use. This bonus is listed lasting 8.5 seconds in power details, and that is accurate for how long that actual boost lasts. The damage boost ends quickly, and just the placeholder counter remains in your 'buffs'.
