What are your current components? What crank and derailleurs? "Upgrading" to 10 speed is relatively straight forward but not real cheap as you would need at a minimum new shifters, cassette and chain if you were willing to keep the current triple crank and derailleurs. Going to 11-speed is a lot more expensive as you would need a new rear wheel, new derailleurs and probably a new crank as well as all of the above.

Perhaps all you really need are a new 9-speed cassette and chain and both are still readily available