Please do.

If you are visiting Bangalore, the Karnataka state(of which Bangalore is the capital) has second largest number of tigers in the country, and there are multiple tiger reserves within 100-150 Mile radius of the city. I highly recommend visiting at least one of them, the forest staff are quite friendly and you can get first hand information on how they deal with poachers etc.

This is the Govt. website so please be gentle :)

https://aranya.gov.in/Static%20pages/TigerReserves.aspx

Bandipur, Nagarhole & BRT reserves are 3-4 hours drive from Bangalore.

PS: Avoid the weekends if possible.

The best chance is possibly Ranthambore. It's close to Jaipur as well (which is on most tourist itineraries) and easier to access than other reserves. It's also a much smaller park so it's easier to catch tigers, especially during summers.