I think the key thing here is to look at is increase of bank deposits (I.e. money for you and me). That is M2 MINUS central bank reserves and notes and coins in circulation. If you look at this you'll see that bank deposits have only increased modestly despite the large increase in M1. From this you can infer that the FED's "money printing" isn't really affecting Main Street very much. I.e. currently not causing much inflation.
What's happening? The FED is creating new reserves and using those to buy bonds. The reserves remain in financial institutions and should incentivise banks to lend - or at least that is the theory. Lending is how bank deposits (money for you and me) are created. The reserves which the FED creates to buy bonds (which are assets of commercial banks) doesn't end up in people's Bank accounts (which are liabilities of commercial banks). Instead, the reserves remain sloshing around in the banks.
My view is that money supply is endogenous. That is, new bank deposits are created when new loans are made. Currently, there is not a demand for loans so there won't be a huge increase in the M2 money supply as a result of these FED bond purchases. Perhaps demand might increase in the future, in which case the US will see inflation. I suspect once the economy recovers and inflation (as measured by the FED) increases then they'll start performing open market operations to sell the bonds they bought and thus remove the excess reserves from the financial system.