For security and email delivery, I recommend you always handle bounces.
If your form is spammed or compromised, receiving bounces is a good way to quickly detect this. I investigate spam related incidents nearly every week for people who have compromised web applications. If the bounces go to an account that you monitor, you can quickly spot an update in bounced emails and spot the issue.
Users make typos and email will bounce. You've not mentioned what you doing with the form, but if you are collecting emails for future use, then you will want to purge your email list of any bounced emails.
I've seen many lead generation systems that do not properly handle email bounces. As a result, you pollute your list with invalid emails. When you then email this list, your get bounces again. This lowers your server's sending reputation and can negatively impact email delivery.
There's also a business benefit.
I do IT support work and people contact us using a form on our site.
Some people contact us about email server issues using an email address that goes to the problematic server.
We used to get calls saying they contacted us but we never responded. Since we monitor bounces, we can call them and follow up.