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Although there is no way to shrink the bin folder, you could shrink the database. Since Sitefinity stores previous versions of a page in the database for versioning purposes, you could shrink the size of the database by deleting these pages. For more detailed instructions, take a look at this database shrinking
For hosting options, Discount ASP.NET also has a database shrink tool
and we do recommend them as a host. For deploying instructions on Discount ASP.NET, take a look at this deployment article
I hope that my suggestions help you host Sitefinity. If you have any other questions, feel free to contact us.
the Telerik team