Dream symbolism can be a tad tricky. The theme I picked up about your dream is the following: The attempt to keep something contained/ controlled that pose a threat. However, it ends up running/hiding and now out of your control. Is there an aspect of your life you're attempting to control and it isn't working out as you had planned. It is now out of your control.
Your dream also indicate that you're a thinker, planner. You're a solution based thinker, not a reactor. Your reaction wasn't impulsive. You wasn't trying to smash it or hit it with something. You took great thought to figure out a way to safely contain the spider. The white spider may be a symbol of the rarity of what you're trying to control/ deal with in your conscious life.

Hope this helps some. Sweet dreams
Belle