Today I took another attempt and was successful. Now I got a secure wireless connection in bridge mode. I wanted WPA because it is much more secure than WEP and in bridge mode it is easier to reach all my devices. Here is my configuration:
nvram set wl0_mode=wet nvram set lan_ifnames="vlan0 eth1" nvram set wan_ifname=vlan1 lan_gateway=192.168.1.254 lan_dns=220.127.116.11 ifdown wan nvram set wl0_ssid=MYSSID nvram set wl0_channel=7 nvram set wl0_akm=psk nvram set wl0_crypto=aes nvram set wl0_wpa_psk=WPAKEY nvram set wl0_auth=0 ifup wan; /sbin/wifi nvram commit;
For more information about the parameters see the OpenWRT wiki.