I don't think you can do this. The "/" filesystem in DD-WRT is Squashfs, although that's not easy to find out. That means that during a build of DD-WRT, a whole filesystem image gets set up, and then compressed in some manner, which renders it immutable. That way, the root filesystem fits in a router's small amount of flash.
A few config files are on read/write storage on /tmp, which is ramfs on my DD-WRT router. /etc/resolv.conf is a symlink to /tmp/resolv.conf, All the crontab stuff is links to /tmp, /etc/hosts is a symlink to /tmp/hosts.
It's not clear what you want to do with the file in /bin, but about the best you can do is scp the file to /tmp, and run it from there. You could re-generate a whole Squashfs filesystem with the file in /bin, and re-flash the router, but that seems like an awful lot of work.