Budget, Budget Car Rental charged me for excess insurance, which I had declined, more than doubling my original quote to a staggering $1800. Las Vegas, Nevada

I rented a car from Budget, having found the cheapest quote online. When I picked the car up with my girlfriend I was asked if I wanted to pay for extra insurance, which I declined, due to it costing over $20 per day, and also as I already had the cover through my own insurance company in the UK. I then signed the rental agreement and left to get in the car.

When we got to the car we noticed no license plate was present but instead a permit in the window, valid for two months as the car was brand new. However, this was due to expire in a couple of weeks and we were renting the car for five weeks so we had to switch to a different car.

I did not sign an agreement for the second car but left in it and returned it after the five weeks. Upon my return my bill came to approximately $1800, double my original quote. To my disgust, in my original agreement a charge for the insurance I declined verbally had been added. 

I requested the money be reimbursed and also stated that although I had signed the original agreement, that was for the car that I didn't end up taking and so was of no relevance to the car I took. Budget have stated this agreement can be transferred between cars without any agreement from myself. 

I have requested a copy of the terms and conditions that state the above but they have not supplied me with them or directed me to the relevant page on their website. I also requested a copy of the CCTV footage they claimed to have reviewed, which I know would show we declined the cover, but they have refused. 

Both my girlfriend and I are upset with how we have been treated. There is no way we would agree a charge that would double the fee agreed originally and can not believe how a company like Budget can dishonestly take money that I have worked months to save like this.

I accept that I should have read thoroughly the original agreement before signing but do not expect to have to do so having verbally declined the extra cover that was offered. I would be extremely grateful if anyone could direct me as to which way to turn as I am unsure of the US legal system with me being from the UK.