IMO the effects of a further recession on bitcoin would be very interesting.
Recessions are generally triggered by the markets waking up to the fact that some financial asset is not worth its price, despite being directly or indirectly propped up by the state (e.g. the stock market is indirectly propped up by low interest.) For one reason or another (maybe because the effects are expected to be mild,) the authorities decide to let markets take their course this time. (As opposed to 2008 when they pulled out all the stops to save the "troubled" bank assets after deciding, wisely or otherwise, to let Lehman Bros. fail.)
Asset prices go down, people lose savings and consume less, leading to job losses and further cutbacks of consumption, etc. etc.
Now the key question is whether the core world system will hold, i.e. whether the public continue to have confidence in the money issued by the central banks. In practice, we probably also have to count Western public debt and bank deposits as money -- allowing these to crash while protecting only currency would mean a lot of economic pain and thus be politically unfeasible.
If the core system holds (and the very fact that the authorities allow a market correction means they expect it to,) then every other asset is in effect an investment. Investments tend not to do well in recessions, since the prevailing climate is a shortage of money to go into any investment, and a tendency of money to go into perceived safe havens like dollars and Treasuries.
That said, certain investments are special cases. Gold, silver, and now bitcoin have the potential to become reserve currencies, being naturally limited in supply and possessing other properties of money. And it doesn't take an imminent meltdown of the core system for their values to go up. If there is a significant chance of either a meltdown (and note that the longer the current system lives on, the more uncertain the answer will be) or prolonged economic pain which becomes politically or otherwise unsustainable, the authorities may decide to peg their currencies against these limited-supply assets, for the safety of the world system. And they will have to peg at a very high price of these assets, to give themselves room to push stimulus and reflate the economy. But they will not let us know until the very last minute.
Even if there is just an increased chance of this happening, these assets tend to see increased demand. I suspect this was why gold went up several fold during the Great Recession even though the core system held (at least it seems so far.)
I guess this is a long-winded way to say we don't really know!