They don't tell you that you are unlikely to see tigers in these National Parks. You go there believing you will see at least 1000 of the 1411 tigers still left. However, if you want to be sure that you see tigers and lions, the place to visit is much closer home. Bannerghatta National Park, anyone?
Just take a Vayu Vajra Volvo bus to Bannerghatta National Park on a leisurely weekend. The bus drops you right at the gates of the park. Don't expect to see too much of jungles like Bandipur or Nagarahole. Remember, this National Park is closer to Bangalore than some of residential apartments :-) You need to buy tickets for lion-tiger safari and board the safari bus operated by the forest department. The safari is very similar in structure to the ones you see in Bandipur or Nagarahole, though there is less jungle all around and much more chance of seeing animals. The animals of Bannerghatta are not afraid of humans. They stride carelessly into the path of your safari vehicle. They might even give you a bright smile when you take a picture! The driver may sometimes need to honk and make way through the group of tigers who have assembled right in the path of the safari to hold a meeting or something. The safari lasts about 45 minutes.
Once back, take a stroll through the zoo (which is the inverse of safari, they are the ones in cages!) to see other animals. Then buy something to snack on in one of the numerous shops and head back to the bus stop. See, you didn't have to sweat even as much as you would to catch the greatest deals during a sale in your favourite mall and costed even less!
None of this is to say that it is not worth visiting the real serious National Parks elsewhere. Go there to experience closeness to nature without any expectation of seeing these animals so you won't be disappointed. When you want to be sure to see the animals, you know you won't have to go too far.
