Hi Mackenzie,
This is a problem I have tackled because my museum is located in an old soda factory. We have lots of glass bottles! The best economical solution I came up with that has worked for the majority of our bottles is to use trays inside of a standard record carton and tissue paper to provide padding between each bottle. Depending on the size of the bottles, I can fit 5-6 bottles per tray this way. The bottles are stored on their sides this way, not standing up, but I do not have the space to store them upright. I use enough tissue in between that they do not move at all, so this has worked out well for us.
Hope this helps, and maybe others will have ideas too!