I agree that a parts bin is a bit much. Most people I know that have one can't find anything, and don't remember where half there stuff came from if they can even find it...
Regrettably, I also don't think I would care much for taping the parts to a piece of card stock, as it just seems a good way for a part to come off.
Instead, I use 2x3 resealable bags, with the Name and IWM Catalog number on them (created with a label maker)...
These little packets allow me to store all the parts from one mech in a single place and I can add or remove parts easily without having to have them spread out over several boards. Plus, an empty packet tells me that I need to order more of a certain part and/or if I am writing a "How to" I know where the part came from... Then to store them, all the little packets go into a Plano Model 3730 storage box, and I sort them alphabetically which makes finding a part quicker... I use this same system to store Mechs that I bought second hand, that way the parts are always with the Mech and I don't have to go looking for them.
As for cost, I can't say my way is the cheapest... While 100 of the bags cost $1 USD at Wal-Mart, the label making process burns through a lot of the label material. I can't tell you how many of those cartridges I've gone through, but it has been quite a few and they ain't cheap.
Caz
Edit: Sometimes, when I read what I've posted, I would swear English is my second language (which it isn't).