I've been wearing my old (chamois-lined) bike shorts on the bike, and put on warm-up pants for other exercises, to avoid scaring the children and grossing out the adults. I may just buy another pair of bike shorts, new, so that the Lycra in not shot, and use running shorts over the top.

The lumps in the padded versions are aesthetically unappealing in poses that include stretches, bridges, planks, ans such.