It's a power-density thing.
Steam could be used to power a bike engine. Ideally, the steam would spin a two stage turbine, (steam output from the high pressure turbine would be fed into the input of the low-pressure turbine) where the shafts are coupled, and the shaft of which would be geared down to something usable to drive the bike. But, you would probably need several hundred PSI steam pressure. So, you have an externally fired boiler, a water source, a low volume high pressure pump to inject water into the boiler to maintain the liquid level a burner, a fuel tank... Now, an external combustion engine (which a steam engine is) is much cleaner than an internal combustion engine. Of course, if you're trying to use batteries and an electric heating element to generate the steam in the boiler, you'll have issues with electrical storage capacity.
Steam has it's own issues. First off, it's corrosive - especially if it's not pH neutral. Second, any minerals in the water get left behind in the boiler as the water boils away, so there are issues regarding scaling (mineral deposits when the mineral levels get supersaturated in the boiler water.) You have to have some sort of level control, to automatically keep the hot water level in the boiler stable. You have to fire up the boiler well in advance of actually going anywhere, too.
You could use a piston-based engine, (probably based on a 4-stroke gas engine) but, in order to get any sort of efficiency, you would again want a two-stage design, with essentially two separate engines with mechanically coupled output shafts, where a small cylinder high pressure engine is used as the primary stage, and it's output steam is fed in to a large, low-pressure steam engine used as the second stage. Think of using a Honda GXH25 as the primary stage, and a GX160 as the low-pressure stage. 200 psi into a 1 inch cylinder, and 50 psi into a 2 inch cylinder. Both would generate the same thrust...
Steam can be quite efficient, but, at larger scales - think power plant scales. Even at locomotive scale, internal combustion engines are more efficient... (A diesel-electric locomotive can produce much more power than a steam locomotive, for instance.) As the power plant gets smaller and smaller, the efficiencies get lower and lower.