Peter, can I operate two business names from the same log in, just toggle between them, do we have to pay twice for the add ons?

Ok. Are you a limited company?

Ok.
Bullet isn't setup for partnership business. It's a old type of company.
Then the other company is a sole trader company.
As a sole trader you are the 'company' the money in/out is yours.
So the concept of two legally different doesn't really exists with sole-traders.
Normally I'd say just use the different invoice templates for each company you can't have separate bullet accounts as that means you've separate companies.
But seeing as your in a partnership that's VAT Reg and a sole trader that isn't you'll need two separate accounts with two separate logins.

I'm not sure what you mean. But, you can't have multiple partnerships or partnerships in Bullet. Your accounts won't be right.