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Can I use the BR340 bridge (root bridge) and one AP350 (nonroot)to connect two LAN segments?
NO you can not.
To get an AP to associate to a root device it needs to be in repeater mode which will disable the ethernet port.
To connect 2 lans together you need 2 Bridges (part number AIR-BRXXXXX where XXXXX is the model and series number such as 340 350 or 1400)
BR340 and BR350 on the same radio network is NOT supported
For a short indoor link and less than 8 MAC Addresses on the remote LAN you can use a Access Point and Work Group Bridge.