Why are there only two options? Earlier you indicated that you were considering paying off the balance in the next month or two, that would be option #3.

The amount of money you "save" is really of no importance. What you need to determine is the opportunity cost of the cash today vs 15 months from now. If it's just going to sit in the bank, there is no way you'll earn enough interest to cover the 3% BT fee. Since you're paying it off in a year investing the cash would be quite risky (same reason why retirees reduce exposure to stock market). Also consider that if you can't pay cash today, but you can pay it in 2 months you will have incurred $240 of interest. If the BT lets you get out from under the interest at least 1.5 months early you break even on the BT fee. Although if you put it on your CC you'll get at least 30 days of float.

Other things to consider, check to make sure that payments to the store will count as purchases and not cash advances (since you're technically paying off a debt). Is it possible to return the ring? If you're not planning on proposing for a few months you could buy it at a later date and save the interest in the interim period. I also wouldn't be surprised if they become a little more flexible with the prospect of losing a sale.

Last thing, if your credit is good enough to churn CCs, why would store financing reject you for 0%? It is my impression they are much more liberal with their credit as it is tied to making a sale. Seems kind of odd.