Whatever silica there is in balsa, it'll have little or no meaningful effect on stropping. I think balsa's best attribute for stropping is it's affinity for embedding and holding compound, of which it'll embed quite a lot. This means a loaded strop made with it is very aggressive for polishing; you'll see this in how quickly it blackens after some use. For the same reason, it's also a little more 'needy' of regular maintenance (cleaning, resurfacing), as it'll load up very fast with swarf. Another part of the 'neediness' of balsa for resurfacing is due to it's relative softness, which means it's more easily dented, nicked or cut in use. So it takes a little more TLC to keep it in shape. I prefer something firmer than balsa for a wood strop, like basswood. As with balsa, it's readily available at craft/hobby shops, and is often pre-cut in sizes ideal for stropping.
Bamboo is notoriously high in silica content; it's known to damage woodworking tools & bits used to cut & mill it. But silica isn't necessarily a good match for cleanly abrading or polishing modern cutlery steels. I've got a bamboo backscratcher stick that I picked up at a local store a while back. On a whim, I tried stropping one of my knives on it one day (something simple, like 420HC), and didn't like what it did to my edge, leaving it more damaged (burred, rolled) than refined. Had to take it back to a stone to restore it. Point being, the 'abrasive' silica present in the bamboo was enough to have an effect, but it's not really hard enough to cut or polish such a steel very well. Instead, I sort of equate it's effectiveness with that of millions & millions of microscopically-sized ball-peen hammers beating & bludgeoning a fine knife edge to an ugly mess, with most steels used these days. May sound jaded, but I keep coming away with that same impression, each time I've tried something like bamboo or your average rock on the ground, for sharpening or honing modern steel. There are some exceptions, like the silica-based novaculite in Arkansas stones. But the exceptions are in the minority.