Since there can be no FDIC in bitcoin, people will probably not want to bank with a bank that only keeps a 10% reserve because if there is a bank run, they are forked.
They won't be able to get their money immediately, but a bank can easily prevent a bank run from being particularly disastrous. What they have to do is explain in advance what their bank run policy is and have sufficient assets of some kind (which can be loans) to cover the run in the long term.
For example, if the prevailing interest rate is 4%, they can have an "emergency run interest" of 9%. If there's a run on the bank, they declare an emergency and cover withdrawals with 9%, fixed-term notes. Sure, some people won't be too happy to have these notes instead of bitcoins, but their value will likely be a bit higher then the corresponding number of bitcoins, so they could likely sell them for a slight gain.
This assumes the bank isn't in danger of going out of business. This means the loans (or other bank assets) must still be sound. This can only cover a short-term liquidity run problem, not a long-term solvency crisis. (It wouldn't have helped with the bank failures we saw recently.)
However, a bank can easily cover a bank run with non-cash assets. This is another way commodities can be used to inflate the money supply. You might not trust a bank to keep only a 10% bitcoin reserve, but if they had a billion dollars worth of gold or also owned many stable businesses, you probably would. So a bank can leverage any other asset to allow them to put more bitcoins into circulation than they could otherwise.