Short answer: Yes, but it depends on the size of the fish and the cyclist, and their speeds.
There is a nice published summary for energy cost (J/(kg * m)) for fish, and running or flying animals in this paper in PNAS which suggests that large fish are more efficient swimmers in terms of energy cost per unit of mass per unit of distance. According to this summary, typical values are ~1.5 J/(kg * m). Fish mass will relate more or less directly to their size and aerodynamic resistance. Bigger fish IE sharks will probably be more efficient still but I suppose it is hard to perform experiments on them.
Regarding cycling, the problem is that the mass actually has only a minor effect on the pedaling efficiency on flat ground. This study shows that energy cost for unit distance follows the relationship of (E = (0.606*V^2) + 29.56) where E is the energy cost in J/m and V is the air speed in m/s, on a racing bycicle with normal wheels.
For an enthusiastic cyclists speed of 30 km/h = 8.33 m/s, we thus have an energy cost of 71.6 J/m which may be approx ~1 J/(kg*m) if our cyclist weighs ~72 kg.
Thus, a 72 kg cyclist on a race bike at 30km/h is about ~30 percent more efficient in terms of movement energy than a ~ 1 kg fish swimming at average speed.