The actual outer surface of bamboo is denser than 98% of the woods found in Archery.
Pretty sure sinew can be stretched more when used properly on just wood.
I hope you don't think your simple test proved inconclusively how much bamboo stretches on a wood belly.
You're right that the outer surface of bamboo is really dense and strong. If you use that as a backing, the neutral plane will come very close to the backing in most cases, as a result of which it won't stretch a lot.
Now back to the plant fibers: flax has a SG of 1.4 to 1.5 (just like most other plant fibers), and can stretch up to 1.8% (twice as far as most woods), but some sources mention 4% (but I doubt that's entirely elastic stretching). It has a very high modulus of elasticity (MOE), meaning it requires a lot of force to stretch, unlike sinew. So if you use sinew as a backing, you need a lot more of it to take the most tension of the back of the bow. Since it also has a higher SG than wood, you add more mass to the bow than if you were to use plant fibers (and achieve the same increase in stiffness of the bow, as you would need less plant fiber backing to achieve the same goal).
Some time ago I estimated the max strain of sinew at the back of a 90# turkish horn-wood composite bow. This came close to 5%. That's also close to the elastic maximum for sinew (it can take a lot more, but it doesn't spring back immediately beyond this point).
On many sinewed wood bows, the sinew will not need to stretch beyond 2% (I will try to estimate these as well, but need thickness of maximum bending portion to do so in addition to an unbraced and fully drawn profile pic and ntn length), so in those cases you may also consider a thinner plant fiber backing, yielding in theory an overall lighter and therefore faster bow.
Granted, on very short bows the cost of excess mass is much lower than on typical-sized bows, so you might stick to sinew there. The goal of my post was mostly to indicate that there are other very useful and much easier backings than sinew.