It could take a while to save up that much cash, but I say go for it! I am kind of doing the same thing, trying to save $5000 by designing logos part time. You may want to park the money in a money market account so it would get about 5% interest and you could pull it out whenever you need to. It won`t make you rich, but by the time you have the entire $10,000 saved you will not have lost any money because of inflation.
All banks are different but usually you will not get more than 1-2% from a money market unless you have a really high account balance. MM`s also require a minimum balance of $2k-$5k.
Your best best will probably be an online savings account, such as ingdirect.com, there is no minimum balance and you will get 4-5% interest.
Capital One has a money market account that is gving about 5% interest. ALso as someone said earlier so is ING Direct. Check with your local banks as well. They may have an automatic savings program that can help you save the money.
The main thing is to remember what the money is for. Do not tap into it for any reason. Life will come at you fast, if you are serious about the business then do not fall to the temptaion of tapping into the savings account specifically for the business.
Is the $20,000 you plan to save for working capital or living captial? Make sure you are saving money to live off of as well.