Can I do minimum upgrade to get my bike to fit 11 speed cassette?
Nope. You'd need derailleurs, crank set, shifters, cassette and chain at least. Given that groupsets bought as separate components cost a lot more than they do as part of a complete bike, I almost always recommend buying a whole new bike to make this upgrade.
Can I downgrade my trainer cassette to 9 speed to match my bike?
Yes! All you need is a 9 speed cassette and a 1.8mm cassette spacer.
11 speed road hub freehub bodies are 36.75mm wide, 8/9/10 speed are 34.95mm, hence the need for the spacer (on the inside of the cassette).
All Shimano and SRAM 8/9/10 and 11 speed cassettes use the same 'Hyperglide II' freehub body spline pattern, so the new cassette will go right on.
You will need a chainwhip tool, cassette lockring tool and a big wrench to change the cassette yourself. The tools may cost more than the cassette itself, but a good bike repair shop will do it for you quickly and for a nominally small fee or for free if you have a good relationship with them and buy some small items at the same time. (Disclaimer, that's my experience in the USA, YMMV elsewhere in the world.)
You may find you have to adjust the rear derailleur indexing a little between the trainer and rear wheel as the hubs on each may not laterally position the cassette exactly the same relative to the bike frame.
Another consideration: if your chain is getting worn (a $10 chain wear gauge is a great investment) it would be a good idea to replace the chain along with the new cassette. A worn chain accelerates wear on cassette sprockets.