Why did Bruce get suspicious of Oswald?

More superficially speaking, Bruce suspected Penguin because Penguin's rise to fame was, well, suspicious:

1. A Red Triangle member kidnaps a baby in broad daylight, but gives up the baby to the Penguin in seconds. Why would a crazed gangster be afraid of a short stocky man?
2. Max Shreck inexplicably goes to great lengths to protect Penguin's reputation and privacy.
3. when Penguin is busy with research, the Red Triangle gang are nowhere to be seen, and the streets are, as Alfred remarks, "notably quiet." This could easily be (and is) because Penguin was their leader.

A bit more deeply, Bruce, being an orphan, sympathized with Penguin's desire to find the parents who abandoned him (scene where he and Alfred watch Penguin's staged heroism on TV). Curiosity may also be why he paid such close attention to Penguin, even from the beginning when the suspicious circumstances had not built up yet.