Can an IAS officer take study leave to do a Master's at Harvard, and what bond and rules apply?

Yes. The All India Services (Leave) Rules, 1955 read with the DoPT study-leave guidelines permit AIS officers to take up to 24 months of study leave (12 months in one spell, extendable; 36 months total in a career), with full pay and allowances, after completing 9 years of service (6 for NE cadre officers). The officer must sign a bond to serve the government for at least 3 years after returning, refundable on default. Programmes like the Mason Fellowship at Harvard Kennedy School, Yale World Fellows, Princeton's MPP, Oxford's MPP and LKY MPA at NUS are popular choices.