Don't know anything about budgrafting, Hank, but I would have mixed the straw and nettles in the bin rather than layering them. Straw is a dry matterial that will take time to rot down completely. It could create a barrier between 'stuff' at the bottom of the bin and 'stuff' that you may add later.

You do normally carry out budding in June, but it also depends on the state of the buds and the receiving tree. (Having written that a quick 'google' says August as the best month as the bud remains dormant until the next spring! But I have successfully done it in early summer, so you can take your choice!) As long as the buds are plump and ready to grow away and there is plenty of sap rising in the receiving tree, you should be successful.
Good luck! There's nothing better than seeing a graft or bud grow away and know that you've achieved your aim. Last year I grafted six late apple varieties on to some Malus baccata trees I'd grown from seed and was astounded that five of them actually 'took' (and are growing healthily away a year later!) My first effort some years ago ended in abject failure and I ended up doing a 'saddle graft' instead that did work.

Thanks, Guys, No sooner asked than answered. I'll do as both of you recommend.