Has anyone considered the angle that maybe spending 24/7 in a rather sterile spaceship can make you partial towards "little spots of nature" to reconnect with something "natural" and "organic"? In my experience humans who spend a lot of time cooped up indoors with nothing "green" in sight tend to try to compensate for this in some way. Think potted plants in the office. This might just be more pronounced/exaggerated on starships, don't you think? If you discount the Arboretum and the ("fake") nature on the holodeck, there's not much "nature" on the Enterprise. So maybe the crew tries to make up for that. That would also explain why plants seem to be such a popular gift in the ST:TNG universe...
It would also be interesting to see whether non-human crewmembers share the "plants by the bed" thing. Data acquires a bed at some point, but AFAIK he has no plants near it/ at its head. And what about, say, Worf? Do we ever get to see his bed, and does it have plants? Troi is half-human after all, so maybe human nature is a factor.
As to why the plants are near the bed: Maybe it's just convenient. (You see them every evening/morning, less chance to forget to care for them, if 24th century plants need watering/trimming/fertiliser. Since Keiko's orchids apparently recquire active care I think it is reasonable to assume that they do.) Or maybe it adds to the "view"? Space + plants = prettier than just space? Or it's a left-over affectation from the days of the good old Terran windowsill, as a classical plant-space? Or, a less "esoteric" reason: Starfleet regulates these things, and for some (possibly emergency-related) reason, plants may only be placed in certain parts of/places in your quarters.
I know that this question is old, but I just felt that this angle deserved to be mentioned.