No. You can only ever take one bonus action on a turn.
The scimitar of speed lets you use your bonus action to make an attack, regardless of what you do with your action:
In addition, you can make one attack with it as a bonus action on each of your turns.
However, the rules on bonus actions state (emphasis mine):
Various class features, spells, and other abilities let you take an additional action on your turn called a bonus action. The Cunning Action feature, for example, allows a rogue to take a bonus action. You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus action. You otherwise don't have a bonus action to take.
You can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available.
The scimitar of speed doesn't grant you a bonus action; it gives you a way to use your bonus action. You might have a million ways to use that bonus action, but nothing in the game (so far) ever changes your limit of 1 bonus action per turn. (Contrast the fighter's Action Surge feature or the haste spell, which do explicitly let you take an additional action on a turn.)
There is no "specific" rule of the scimitar of speed that changes the limit on the number of bonus actions you can take in a turn.