Everyone can get online billing, but I'm pretty sure it's not possible to see bills online and get paper bills too.
To get an online account, you'll just need to create a 'My Virgin Media' account for the the billing account and then choose e-billing. You can't use an existing My Virgin Media account email address to register with though, each My Virgin Media account needs a unique username.
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I work for Virgin Media - but all opinions posted here are my own