Does it matter which side I place the bulb in a circuit?
As far as a simple circuit like this is concerned, there is no difference. The three components that make up the circuit (battery, bulb and switch) are all connected in series.

This is of course a simple ideal case (which is perfectly OK in a pure circuit theory point of view), presumably in an hobby context. 

If we consider what this circuit is connected to outside its ideal world, it depends on the context. For example, if the battery were not a battery but a earth-grounded power supply and the bulb had a metallic enclosure also connected to earth-ground (safety ground). These external connection would matter in some cases.

Anyway, as long as the circuit exactly represents what it shows (a real-world 9V battery, a light bulb and a switch), then what I said still stands.

Note: my emphasis about when these circuits might not be equivalent is prompted by my impression that you are a newbie. Sometimes newbies post a circuit that don't represent exactly what's in it. Or sometimes also they think that the answer is easily applicable to "slightly" different situations, and this brings up safety concerns. For example: what I said could be applicable also if the battery were a household power outlet, but only in theory (the theory where the power outlet is seen as a simple AC voltage generator). In practice, in such cases there are safety issues to be considered which call for a deep understanding of what's the real environment "where the circuit lives".

Another thing to notice is that the position of the switch may matter if you are engineering a product, then the physical size of the components and the routing of the actual wires used for the connections may dictate whether one of the circuit is better than the other, although electrically they will behave the same.