From what I understand, Beanstream has a secure webspace which shoppers are directed to. They use SSL certificates assigned by Verisign. I'm quite certain this should work with almost any shared hosting account but I could be wrong. I'll get in contact with the support team at Beanstream to find out what exactly is required in order to run the script. Based on what I've read in the FAQ, you don't need an SSL server unless you use the Process Transaction method in which case a SSL server is required.
If you'd like to get in touch with me, drop me an email at firstname.lastname@example.org
and I'll look further into this for you.