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If I have Wallet A with one address (call it A1) and Wallet B with 2 addresses (B1, B2), can I send BTC from A1 AND B1 to B2 in a single transaction thus incurring a network fee only once?

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can I send BTC from A1 AND B1 to B2 in a single transaction thus incurring a network fee only once?

Absolutely. A transaction may contain multiple inputs and multiple outputs. The trick will be to get the wallet to do this for you. It will need to be aware of both address's private keys, and be able to let you select which inputs to use. Alternatively, you could construct the transaction manually.

See http://en.bitcoin.it/wiki/transaction

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