Do bacteria with multiple flagella move faster than bacteria with a single flagella? Assuming the flagella are at the same length.
Note: in the following I'm going to focus on E. coli, which is the best understood system for bacterial flagellar movement. It would be interesting to compare uniflagellate bacteria and bacteria that have a fixed number of flagella. However, I know about E. coli and I think there is something interesting to be learned just from them, so I'll continue.
You're in luck that you asked this question when you did: a very cool paper (1) was published just last year addressing your question. They find that the number of flagella has only a small effect on bacterial motion, but to understand why requires some background (A lot of the following background comes from this paper, which summarizes it pretty well).
I would argue that E. coli movement is one of the best-understood examples of cell movement we have, with excellent, high-resolution, quantitative data being generated for over 40 years now (the king in this field is Howard Berg at Harvard, if you want to learn more just read a recent review from him).
E. coli have a variable number of flagella, from one to ten or so. They operate in a bundle, but this bundle is highly dynamic due to the way E. coli moves. Rather than proceeding continually a straight line like a car, E. coli moves by a series of starts and stops called a run-and-tumble: the bacteria moves in a straight line for a short amount of time (a run), and then it stops in its tracks and changes direction (a tumble) before starting off again (2). At a first pass this run-and-tumble behavior is essentially diffusion, the bacteria covers a lot of ground without going anywhere on average unless there's some food nearby, in which case the run-and-tumble is slightly biased so that the bacteria drifts toward the food.
As I said, during runs the flagella are bundled together and all turning counter-clockwise. A tumble happens when the bacteria sends a signal to the flagella to start turning clockwise. This breaks apart the flagellar bundle and sends all the flagella in different directions. Up until the paper I mention above, it was still not clear exactly how many flagella need to start turning clockwise before the bundle breaks up and a tumble commences.
Now you can see why having more flagella might not necessarily be a good thing: you might be able to move faster during the run (though this is not obvious to me, given the sometimes unintuitive nature (3) of low-Reynolds number fluid dynamics) but at the same time the flagellar bundle will be more sensitive to break-up because with more flagella come more opportunities for one to start moving counter-clockwise and mess things up.
As the authors of the above paper (1) find, it turns out that there are correlations between the actions of different flagella in a bundle, so that a bacteria with many flagella effectively acts like a bacteria with fewer flagella. The result is that the overall pattern of run-and-tumble is not much affected by the number of flagella; you might argue that number of flagella has a minor effect on bacterial movement.
On the other hand, you might be interested not in the net movement of a bacteria, but just on its speed when it's moving forward, in the run phase. Unfortunately I wasn't able to find any good measurements of the run velocity of a bacterial cell as a function of number of flagella. But hopefully given this recent paper, maybe such measurements are on the horizon!
(1) Mears PJ et al. (2014) Escherichia coli swimming is robust against variations in flagellar number. eLife 3:e01916.
(2) Turner L et al. (2000). Real-time imaging of fluorescent flagellar filaments. J. Bacteriol. 182(10): 2793-2801
(3) Purcell EM. (1977). Life at low Reynolds number. Am. J. Phys. 45: 3-11.