I do not want to get billed twice in span of two months.

Can you sign up for "free" and have it automatically jump to the next pricing level, or do you need to sign up on your own?  Also, when are we billed?  I have a form I will be running for 2 weeks but I do not want to get billed twice if it spans two months...

You can sign up for a free account and continue using it. If you exceed limit of free account, you can then upgrade or downgrade your account anytime you want. 

Please note that JotForm is a subscription based service. Once you upgrade your account, it remains active until you cancel it yourself. If you do not want to be billed for next month, you need to cancel your subscription before your renewal date.

Hope this answers your query.

Do get back to us if you have any questions.