Can I integrate this order form with shopify?

Yes, you can add your form with shopify if you wish.

Hi,
What I actually want is just to create a bank transfer order form to fill out by
customers once they successfully wire the payment.
...

Hello Marie, collecting bank information, credit card info, or any sensitive info using JotForm's plain form fields would be in violation of our Terms of Use.

Here's an excerpt from that page:

Collecting Sensitive Information. You may not use the JotForm to collect certain types of sensitive information, including but not limited to credit card information and any type of login credentials. You may collect some sensitive information such as social security numbers or driver’s license numbers, but you are required to use best security practices of JotForm including SSL and Encrypted Forms features. You are solely responsible for compliance with any data protection and privacy laws and rules applicable to the sensitive information.

You should use one of our payment processors if you wish to process payments within your form.

Related article: Which-Payment-Processor-is-Right-for-Your-Business 

On the other hand, if you wish to get their payment details but NOT charge them immediately, we also have an option for some of the payment processors (Paypal, Stripe and Authorize.net) that works like a Payment Authorization.

Related guide: How-to-Enable-Payment-Authorization