Hi Guy, how would the bamboo be laid if you went that route? Laying it solidly on the concrete floor with adhesive is fine. Gluing it on top of plywood which will lie on the floor will resonate unpredictably and should be bedded down on a mastic.
I would prefer the bamboo solidly installed, a) for its beautiful appearance b) for sound quality.
Carpets being relatively thin will absorb sound only over a very limited range of frequencies, so forming a narrow-band absorber. If the carpet is wall-2-wall the effect will be to largely absorb all the information that corresponds to the wavelength of your carpet thickness. To be clear, this info will be mostly MIA
A thick attractive wool rug or rugs on felt underlay are fine.
However, isn't there always an however? if you would like to add broad-band absorption (this is the good kind that actually does something and not just reduce a little flutter echo) a better way would be to build a cloud but you may need permission.
If you have the height, hang a frame about 4' x 6' x 4" below the ceiling. This will accept standard panels of rockwool or equivalent. Choose a pretty fabric that compliments your room to cover the frame. The winner here is the fact that by varying the distance from the ceiling you can adjust the low frequency performance. Try for 4" air space, but even 1" will make a rather large improvement.
Depending on personal taste, an LED strip light mounted on top of the frame perimeter looks really cool.