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I'd buy a bleed kit (epicbleedsolutions.com) and carefully have a go, then if you fuck it up take it to a different shop.
I think I'm going to give it a go. On the epicbleedsolutions, there's two Shimano kits, but neither mention RS685, one appears a generic pack the other mentions specific Shimano models, am I safe to assume #1 is the correct kit
#1 https://epicbleedsolutions.com/collections/shimano/products/shimano-bleed-kit
#2 https://epicbleedsolutions.com/collections/shimano/products/shimano-road-disc-brake-bleed-kit
I like to tell people it could take longer if things don't go to plan and make sure people are prepared for that, but an hour and a half (£80ish at my rates) is a bit much for one brake, if things go well I'd say it's a half an hour job including getting the bike in the stand etc. It's not that hard really, I'd buy a bleed kit (epicbleedsolutions.com) and carefully have a go, then if you fuck it up take it to a different shop.