Question: What constitutes a Streak Bonus? This is in relation to obtaining the Combat Efficiency Ribbon, which states that you have to obtain 3 Streak Bonuses in a round.

Answer: 
The wording on the bonus is really silly (same goes for the Nemesis ribbon). Once you get 5 kills, you're considered to be a on Combat Efficiency streak. Your 6th kill gives you a 1 streak bonus, 7th kill gives you 2 streak bonus and 8th gives you a 3 streak bonus and hence the ribbon.

It is possible to get multiple ribbons in the one life. Once you have got the first one, (I think) you will get the next one for every 3 subsequent kills in that life.

So if you go on a 23 kill streak you are going to 6 get of these ribbons (8 + 3 + 3 + 3 + 3 + 3)
Combat Efficiency Ribbon 
500 XP Bonus. Get 3 Kill Streaks in one round. To get a streak, you need to kill 8 times in a row without dying yourself. Get 3 Kill Streaks of 8 to unlock this ribbon, try playing on infantry heavy maps to increase your chances early on.

Per <http://www.gamefront.com/battlefield-3-ribbons-guide/>