Thanks everyone for your help. I'm going to conclude that it can't be done with this particular hosting company. As pointed out, that's the drawback of shared hosting....

I'm getting permission denied to exec that. Would that be a bad security exposure for a hosting company to provide that service account name to a customer? If...

Right. I understand the error -it's because I was resolving a server.mappath to some e:\... folder which is on the web server, but not local to the sql server.

Since...

Thanks for your replies. I think I've got the backup command syntax. The part I don't understand is giving permission to the "SQL Server service account". How...