I'm of the opinion that we shouldn't do things like this. Aside from bridging being a clunky and awkward experience for you and your readers that fragments discussion, it's not a good way to promote growth in the new platform. The new platform needs its own identity and exclusive content to give people a reason to move there. If it's just a place to consume Twitter feeds through a different, roughly bridged, interface, there isn't much value there.
By nature of you wanting to copy your Tweets across, you see value in the new platform. If you believe in the new platform, you should actually move across. Readers who actually believe in your content will follow you. If you don't believe in the platform that much, stay on Twitter and don't confuse your readers with two platforms. Straddling the middle is awkward.