What Sniffer said. If you dig from the bottom up, it is easy to get the bottles without damaging them. Essentially, you dig under the dump, and let all the dump stuff fall out toward you. This is the safest way to get the bottles without damage.
But first, get to the bottom. Breakage may occur, but you can't see what's below so you can't avoid losing one or two (privy diggers scratch out every piece for obvious reasons, it's ALL down for them). A quality full length spade shovel is the main tool. Keep digging deeper, the hole will get wider and deeper. Have patience, look to see if it gets older. If it gets good and old on the way down, get scratchin' with a potato rake or trowel, 'cause putting a shovel thru a nice bottle feels worse than most things in life. Keep going deeper. If the stuff coming out don't look so good, or the dump taps out shallow, try another spot. Some dumps with 1950 crap have 1850 crap 4 or 5 feet deeper. Try to keep all the tailings in one pile, so you don't have to move dirt twice. If it's a killer dump, confirm where your tailings pile will be put, so you don't cover up a good section of dump. All this is not an easy task, especially if it is a deep dump. Have patience and keep thinking deeper. If it's in the woods, bring pruning loppers that will cut a 2" tree root, and don't stop till you hit bottom. Hope to see some pics and good luck!