You could pick them just under-ripe and they'd soon ripen up but storing them would be difficult as they are soft fruit and easily damaged. The only way would be to spread them out carefully in a single layer in a large box.
Wouldn't it just be a lot easier to get some fleece or netting and erect it on a temporary bamboo cane frame over your bushes. This would deter the birds. Alternatively use bird scarers such as old CDs hanging up on sticks and string over the bushes. As these spin round they flash and are fairly effective.

cant you make up a frame and put a net over it ?

oops sorry bertie lol

Thanks Bertie and Np. I don't mind sharing some with the birds, but they seem to be beating me to them at the moment. lol. I wandered if they 'would' ripen indoors like toms, because as they are hanging, if you can imagine, they look like a bunch of grapes, the top half is quite ripe, and the bottom still a bit under ripe. So I was thinking to pick the little bunches, as opposed to picking the individual ripe berries. (Being lazy I am really) lol.

i know what you mean but berty is right in the trade if you like for a lot of fruit baring plants and trees they use fine netting as its the only real way of stopping the bigger pests. i have a cherry tree at the end of my garden . i dont like cherries and the tree is a good 30 feet tall with a spread of 20 feet .it gets heaving with cherries . i guess youd get a bath full if you could pick them all at least . im trying not to egsagerate here lol but im about right anyway back to the point lol . theres a lot of fruit is my point but on no specifick day and not perticulerly when the cherries are ripe , as you say just before there ripe the birds come down and strip all this fruit in what 2-3 days easily .anyway you can buy cheap netting from most garden centres and for the frame go to a builders and buy the battoning they use for under the tiles you lay on house rooves.its rough sawn and treated and cheap . its also a good idea if you want to make your own trellis.take care ill stop running on lol bye for now .