I take it your reader shows up on ADE when you plug it into your computer and your computer is authorised ? If so then you should be able to drop and drag from the library onto your reader.
Do you just have ADE loaded or do you have the Sony ReaderLibrary loaded as well? I found that I couldnt get ADE to recognise my reader until the SL was loaded onto my computer.
I dont use the Sony Library but use Calibre (mentioned by carpetmojo above) instead. If you have the books in the ADE library then in your documents folder their should be a folder called My Digital Editions which will contain the EPUB book that was created when you transferred the book to ADE. If you load calibre you can drag and drop the file into it and when you plug in your reader it will recognise your 350 and then you can transfer it that way
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