Forgive me if I'm being presumptuous, but from the way your question is phrased, I'm guessing that you're not currently in Japan, but are planning to come here for travel or work in the future.
Seiza isn't a sitting bow - it's a style of sitting, where you fold your legs underneath yourself and effectively sit on top of your calves. While sitting seiza-style is part of traditional Japanese etiquette (the word "seiza" translates literally as "proper sitting"), in modern Japanese society it's not something that Japanese people are required to do all that often, and it's even less common for foreigners in Japan, for travel or work, to find themselves in situations where it's required.
Seiza has a distinctly old-fashioned vibe to it, and so you'll see it in tea ceremonies, dinner receptions at extremely traditional restaurants, martial arts sessions/performances, and other cultural activities. However, even in these cases seiza is for orthodox, very formal versions of such events.
Again, since you're asking your question in an open internet forum, I'm guessing you're not currently in a position where you're going to be expected to be participating in any ultra-orthodox tea ceremonies or martial arts activities, or dining with Japanese people who expect you to follow every baroque aspect of Japanese manners.
If you're in Japan as a tourist or new-to-Japan business traveler, Japanese people will understand that seiza is something you're not used to and/or physically uncomfortable doing (seiza is uncomfortable even for many Japanese people, after all). Because of that, Japanese people are extremely unlikely to expect you to sit seiza-style. As an alternative, it's acceptable to sit with your legs folded Indian-style. Sitting with your leg stretched out in front of you is something you should probably avoid if you can, though, since it looks a little slovenly and can intrude on other people's space. Oh, and if you're not sitting seiza-style, it's extra-important to make sure your socks are hole-free.
By the way, there is a sort of "seiza bow," in which you place your hands flat on the floor and lower your forehead towards the floor while sitting seiza-style. Again, though, this is an extremely formal style of greeting, generally only done in modern society by service industry workers who are greeting guests in an environment where the guests are likely to already be sitting on the floor when the worker appears (such as traditional restaurants with private banquet rooms or Japanese inns).
「 is it acceptable to stumble a little to the floor? Or would it seem impolite and it must be a graceful move? 」
Stumbling a little to the floor would be "acceptable" in the sense that no one would think you were rude. They would, however, probably be very worried about you, and pretty quickly say something to the effect of "You don't have to force yourself to sit seiza-style if it's difficult for you."
「Would I have to explain my bad leg every time?」
Again, there are probably not going to be any times where Japanese people expect you to sit seiza-style. However, if you do feel the need to explain, you could say "Sumimasen. Ashi ga kega shite sieza dekimasen," which means "Pardon me, but my leg is injured, so I can't sit seiza-style."