Mystery Snails and Lucky Bamboo

Hi, I'm new to aquariums and wanted to set up a sort of mini-aquarium that contains only plants and mystery snails. Before setting up something that could fail I decided to consult others who have more experience than myself. Here's what I would like to do.

I was thinking of purchasing this glass vase/bowl:
http://www.target.com/Cylindrical-Vase/dp/B002YRDOL4/ref=sc_ri_1?ie=UTF8&node=13812701
The dimensions are: Height: 5.2 "; Width: 9.0 " (I'm assuming the width is the diameter).

I would like to purchase maybe 3 of the Mystery Snails from a local PetSmart store. Here's the link: http://www.petsmart.com/product/index.jsp?productId=3954040

I have pebbles that I purchased from Ikea a while ago to be used as decoration. They are currently being used with my "Lucky Bamboo" plants.
I'd like to use these pebbles in the bottom of the bowl, and place 1-3 stalks of the "Lucky Bamboo" in the vase. I've heard mixed comments about "Lucky Bamboo" and whether or not it's safe to cohabit fish and animals with that plant. I mostly read bad reviews with regards to fish, haven't heard anything about snails.

Also, I was thinking of purchasing this (http://www.tomaquarium.com/prod_details.php?cat=29&p=60) filter to use in the bowl since it's advertised as being suitable in only a few inches of water.

The last concern I have is whether the snails will crawl out of the whole setup to begin with. Is this setup a bad idea? If so, how can I improve it so that the bamboo and snails can live together, if that's even possible.

Thanks for any help that can be given!

Hi,

Thanks for the response. I was wondering about that as well. At the lab I work in we ordered some Elodea sprigs and when we received them they were covered in these small black snails. I was thinking of taking some home and placing them in this setup but probably without the filter since they might get stuck. I'm just not sure if that's a good idea...

Great! I think thats what they are since they are football shaped. Do you think I need a filter for the water? Also, do those snails just eat algae?