When Daisy was a pup, I used to reach in her bowl while she was eating, and even sometimes pull food out of her mouth. My wife, who has seen dogs bite, was kind of freaked, especially since Daisy's a pit X. I explained, "I am getting her used to it while she is a puppy, so she'll learn not to bite when someone goes near her food. Either that, or I'll still be able to get my arm back, and I'll learn not to do that again when she's older!". Fortunately, she learned not to do it. We caught the 1 yr old neice taking food out of her bowl while she was eating and hand feeding kibble to her!
To this day, I still grab Daisy's bone from her while she's chewing on it, just to re-affirm who alpha is (that's usually when she looks at my wife, letting me know who the REAL alpha is!). If I pick her up when she's chewing, she'll sometimes growl. This used to make me angry, until I realized that she isn't actually trying to bite me, just let me know she doesn't like it (I'm not sure this is wholly acceptable that she's growls, but then it really isn't fair for me to pick her up like that, either. So I usually hold her for a few moments to make sure she isn't going to be aggressive). What I might be inclined to do would be to grab her food (or whatever makes her aggressive), and if she tried to bite (or did bite), I would grab her by the nose very firmly (not enough to hurt, but enough to know I'm not playing), and get very close to her face and very loudly tell her "NO!" I'd definitly let my actions no I wasn't pleased, then take the food away. I'm a bit of a cement head, so I don't worry about breaking skin (Cheryl still has visuals of the bloody scrapes on my hand from Daisy's puppy teeth, teaching her "Take nice". To this day, however, everyone is amazed how gentle she takes treats), so if you're nervous, put on a heavy canvas gardening glove or something.
I'm not an expert, but this is what has worked for me in the past.
Hagar:"What kind of dog is that?"
Man with dog:"He's a nice dog!"
Hagar:"You know, at the end of the day, that's always the best kind."