Curious as to how tickets purchased as part of Disney resort package can be bridged...we bought our 9-day PHs as part of the deal where you got one day free. So technically, I only paid for 8 days. So, when trying to calculate the upgrade cost, should I use the gate cost for an 8-day or a 9-day PH ticket? And do I still need to use the ticket first?
Disney
ticket prices are highest for the first three days. If you have a 4-day ticket or more, adding one day only costs $10 before tax. So, a 4-day PH is $354, 5-day PH is $364, 6-day PH is $374, 7-day PH is $384, 8-day PH is $394, 9-day PH is $404, 10-day PH is $414.
You would use the 9-day PH ticket gate cost. That's the real ticket you have. The "get one park day ticket free" is a marketing lure. It likely sounded more valuable than $10.

Your 9-day PH is worth $404. 10-day PH is worth $414. Difference 10 + 6.5% tax = total $10.65. You can't upgrade past 10 days on a ticket. You would have to start over at the expensive first three day pricing, or upgrade to an Annual Pass.
As far as price-bridging, there was a ticket price increase Feb 23, 2014. If you booked your package with tickets before that date, you would owe for your one-day upgrade, plus the cost difference between the old and new price of your 9-day ticket. To avoid that extra cost if it pertains to you, use your ticket first to enter a theme park before upgrading. Old package tickets will be price-bridged to current gate price. I don't know if you have that situation, but it's customary for veteran visitors to WDW to advise anyone inquiring about ticket upgrades to use their tickets first, as it can't hurt, and many times it will help.
Upgrade your tickets at Guest Relations (just inside and just outside each park, and 2 at DTD), or at a park ticket booth, but not at your resort.