If you have a single bucket in your hotbar and you right click with it selected on a cow / mooshroom, you hear a milking sound, and the bucket seems to be full. But if you then open your inventory and left click on the bucket (for example to move it from the hotbar to your normal inventory) the bucket becomes empty. And you have to left click three times on the bucket, before you can move it. Or, even worse, if you take an item from your inventory (a stack of dirt, for example), and left click with it on the bucket of milk, the bucket becomes empty instead of exchanging positions with the item. If you then try to put the item back in your inventory, the item seems to disappear. But, luckily, the item isn't really gone. If you close and reopen your inventory, you find the item is on the hotbar, and the (empty) bucket is in your inventory.

Workaround: When milking a cow, right click three times on the cow, then the bucket stays full, and you can normally move it around in your inventory.