When Bilbo awakens, he finds he is caught in the trap of a giant spider, who is creeping toward him. Without a thought, he uses his sword to free himself and kill the spider. This victory leads Bilbo to name his sword "Sting".

When Bilbo goes to find the dwarves, he finds that they have been captured by the spiders too. Bilbo distracts the spiders by throwing stones at them and leads the spiders away from the dwarves by yelling. Bilbo is wearing his ring the whole time, so the spiders can't find him. Bilbo quietly returns to the dwarves and frees them, but the spiders return and the company begins to fight them off. After the spiders suddenly retreat, the company realizes they are in one of the areas used by the elves. They rest for a moment, trying to decide what to do next, when they realize that Thorin is missing.

They do not know that he was taken by the Elves.

This event marks the beginning of a new brave and courageous Bilbo. He doesn't think twice about freeing himself, slaying the spider, and saving the dwarves. His actions save the lives of the dwarves, again. This time, it was not by luck, but by bravery.

When Bilbo first finds the ring, it's magic helps him to escape the mountain. The dwarves look on him with a new confidence. But, this act was different. Bilbo did not rely on the magic to impress the dwarves, he actually stepped up and used his courage. He only used the ring to trick the spiders, when he knew he was unable to slay them all.

I think this is a milestone for Bilbo. He finally realizes what he's capable of. He uses his abilities and the tools that are around him to make quick decisions. This is very different from the forgetful, afraid Bilbo at the beginning of the story.