Is there any way to set up a B2B site so that it does not require a log in/password but anyone could order the product on the site?

PRESSERO > *Pressero FAQs
A site that does not require login to enter would be a b2c retail site, not a b2b private portal. A b2b storefront requires a login to enter and place orders.
 
However, besides a visitor creating an account and logging in, there are two other oprtions:
  • Shared Account, and
  • Single Sign on.
 
Shared Account
You could create a b2b site and have a single user account that is shared among many people. There would be only one username and password to access the site, which can be displayed at the top of the login page. There are five limitations with a shared account:
  1. The order history function is disabled. 
  2. The password and email reset functions are disabled. 
  3. Save For Later is disabled.
  4. Order confirmation emails will be sent to whatever email the shared account is set to use.
  5. The users will not have access to the address book to add or edit addresses if the site's address book mode is set to address book or both mode.
Note: Simultaneous visitors using a shared login account will not see each others shopping cart. If you need or want the customer to be able to return later and see their orders, or order again from the same account they set up, then each user needs their own account, not a shared account.
 
To set a site user account as a shared account, go to Sites > [site name] > Site Users > General Information tab.   Scroll down to the "Additional Information" section.  Click the box labeled "User Account is Shared."
 
Single Sign On (a.k.a. Single Sign In)
If you go with the shared user account idea, you could also put a link on your website that when clicked by anyone, brings them immediately into the b2b site without having to log in at all. You do this by using a single sign on method of passing a username and password into the shared site.
 
Again, if you need or want the customer to be able to return later and see their orders, or order again from the same account they set up, then each user needs their own account, not a shared account.