Your Jetblue flight will arrive in the International Terminal A. All Int term app rides pickups are on the departures level where you exit security. For taxi you would go downstairs to the arrivals level. All similar walking distance.
Uber/Lyft would be fine if you go choose to got that route. I have pretty much switched over to
Wingz for airport runs. You would need to request in advance. Same price as Uber/Lyft but will get you a driver assigned in advance and likely a much nicer and cleaner car. Taxi would be more expensive.
For the return, I would request Wingz in advance for the time you want to go to SFO and then not have to worry about it again.
Enjoy your stay at the Drisco. It has been several years, but that was my SF hotel of choice before I moved to the Bay Area. You will feel like a local. You could ask them about a car, but my recollection is that it is first come first served for for rides and not sure if SFO is included.
If you decide to try Wingz, PM me and I can send you a referral code with a credit.