Most market makers keep some inventory. Just like a supermarket has a stock of food ready to sell. I don't think you can call yourself a market maker and have zero inventory at all times. But it may be that the bond dealer does not have a particular bond.
Let's be perfectly clear that when you sell a bond that you don't have you are now short that bond. So you will lose money if the market price of that bond goes up.
There are several things you can do:
You can quickly go into the market and buy that bond (or a fairly similar bond). If you buy it for a higher price than you sold you eat a loss. Presumably when you quoted 90.2 you were aware of this possibilty (maybe you should have quoted 90.3 ?). If market is very active someone else may want to sell you than bond at your bid soon, so you may be willing to wait a little.
You can buy a derivative like a bond future so you are hedged. There may be a special department whose job is to hedge the aggregate long/short position in this way, although it is seldom done just for the sale of a bond.
You can borrow the bond. Let's keep in mind that this turns the uncovered short position into a covered short position which you can continue indefinitely, but you are still short the bond and are liable for price increases until you buy it. So this does not decrease you risk and is usually done for operational and legal compliance reasons, not risk management.