I'm going to echo Seahorse here, and say head out to Brimham Rocks - I have returned from there loaded with Bilberries more than a few times! (My sister lives in Harrogate, in case you're wondering why someone living in Pembrokeshire heads all that way to pick bilberries! There are lots round me too.)

You're way too early to find any yet though - they are usually at their peak in August, but may be about in July depending on the weather. It does seem to vary more than it used to though, due to our ever changing climate. When I was a young 'un, living surrounded by heather moorland (and therefore bilberry bushes) in the North Yorkshire Moors, the best time used to be around the 'Glorious Twelth', i.e. 12th of August, when the grouse shooting started. It could add a certain excitement to picking!