I'm with
@AndyRM on this. It's bad going if you put the bike in, knowing you're brassic.
I always put mine into the shop knowing I have the money to cover repairs, new parts and anything else, even if I don't have the cash (I hate cash) on me, they get their dues by my bank or credit card.
Getting back on topic, I personally think you should go cap in hand and apologise and tell them when you can afford to pay for the repair. You may find they'll charge storage though.
If you've put the bike in with money, and then had a bill come out, might be worth lining your finances up to come out on a set date, so any remaining money is yours (sorry to step on financial toes).
I'm fortunate I have a good long standing relationship with my LBS, and I have been known to leave owing £3 (they swapped my QR Seat Bolt for an Allen Key based one, prepping for London), but I swiftly paid them for it within an hour or so (I didn't expect them to fit the bolt etc there and then).