Let me back up here and try to be less smarmy and more straight with the facts of the matter.
The primary reason I think your idea isn't favorable to using bcrypt is because of the weight of experience and research. Dropping bits from your salt might be a perfectly valid crypto protection technique, but when it comes to crypto, I'm inclined to go with research over cleverness.
If dropped bits from the salt were a viable means of securing passwords, I'd imagine that someone would have implemented something like this already. It's one of those "oh, that's clever" ideas, but the cleverness trap is a dangerous thing. Just because something is clever doesn't make it good.
This is one of the most oft repeated warnings when it comes to crypto: don't build your own, you'll do it wrong.
The difference is that bcrypt's cost factor is an intentional implementation with well understood results. Truncating part of your key and intentionally brute forcing it is a kludge.
The primary reason I think your idea isn't favorable to using bcrypt is because of the weight of experience and research. Dropping bits from your salt might be a perfectly valid crypto protection technique, but when it comes to crypto, I'm inclined to go with research over cleverness.
If dropped bits from the salt were a viable means of securing passwords, I'd imagine that someone would have implemented something like this already. It's one of those "oh, that's clever" ideas, but the cleverness trap is a dangerous thing. Just because something is clever doesn't make it good.
This is one of the most oft repeated warnings when it comes to crypto: don't build your own, you'll do it wrong.