We never like seeing people go, but if you really wish to close your account, just follow these steps:
Firstly, ensure that you have the right account type - you'll need to have Owner-level permissions to be able to close an account.
Click Settings on the top menu, then the Plan & Billing tab
Under Your current plan, click on the Cancel subscription link
On the confirmation screen, click cancel anyway.
Fill out the form on the next page and click Submit.
Once you've done this, your account will be closed immediately.  Please ensure that you have exported any bugs that you may need to keep a record of prior to closing your account.
Alternatively, if you're only planning on shutting down your BugHerd account for a short period of time, then to ensure that your information is kept in tact, then you may wish instead to Pause your account instead.