You didn't need to put the router in bridge mode - that's used for extending a wireless LAN, but you only need the one device. All you have to do is configure the wireless interface in the laptop to match up with the wireless settings in the router. For security you should first configure the router to use WPA encryption in its wireless interface, and then set up the laptop to match. I presume you use Windows, so I'm not able to help with the specifics of setting up the router.
When the router is set up with the correct wireless settings it will be able to share the internet connection, and the two computers can also talk to each other to share files.