I'm pretty sure that the SQ flight and the UA flight at SIN arrive/depart from different terminals, so this should definitely enter into your equation.

If you have no luggage to check-in, one hour should be relatively safe, but still strikes me as a little bit risky.

Given that hotels in SIN and BKK are cheaper than in BLR, couldn't you do a quick overnight in either city to minimize risk?

If you're dead set on a same day connection, I would recommend BKK over SIN...