I went to Bartender Bailey to accept my daily shadow contract. When I got there, I had a bonus chest to open. After opening this chest, I now have no available daily contracts. 

In addition to a description of the bug you are reporting, please provide:
Device Type: iPhone
Device Model: 13 Pro Max
Device Operating System: iOS 16.6.1
Diablo Immortal App Version: ??? Latest I guess
This needs some clarification…
On a Monday, after weekly reset at 03:00 (server time), there are three bonus chests available at the Bartender, for the first three Contracts completed in that week. Once you have collected these, there are no more to open, regardless of how many more contracts you complete.
Prior to the most recent patch, Shadows used to get three daily tasks, and they had three contracts available on a Monday, with one more becoming available each subsequent day.
Since the patch, we now get 20 tasks to be completed in a week. These can, and will, still ask for Contracts to be completed. However, this does not alter the fact that the Bartender still only offers bonus chests for the first three contracts completed in the week.
So, as it’s not a Monday (when three contracts would be offered), if you’ve completed today’s Contract (Friday), you won’t get another one until tomorrow (Saturday).
I have not completed 3 shadow contracts yet. I have only done one. And there was a contract available and a bonus chest to open. I opened the chest first and when I got back to the contracts menu it said no contracts today come back tomorrow.
You forgot to tell if you saw all/any more chests. Seems you opened the other 2 previously in the week, and not the third, then after the third, the game should show all 3 opened (if you have new contracts) or that message to return next day (if you did all available contracts and got the 3 chests’ rewards for the week).
As @Meteorblade mentioned, the 3 extra chests reset each monday (unless last update changed things a bit, we will see next monday).