I know I'm necro-ing this thread, but the OP's question was never really answered. Partial bypass is indeed possible, and if the only bleach you have is a blix, then you can still do a partial bleach bypass. Bleach bypass is also reversible, so you can keep removing silver while you experiment until you have a silver density you like.
Given the original question, I'm assuming you have blix and straight fix, but no straight bleach. I'd try using no blix first to see how you like it. If that produces too dense of negs for you, blix it for 10% of the time, then refix. Repeat until you have a process you like, then do it with negs that actually matter.
Though if you're going to all this trouble, you may want to get a separate bleach, since there's no reason to use blix except convenience, and this is decidedly NOT convenient. Still, I like the look, and it's worth working for! :-)