Should you put radial tires on a 1997 Honda ST1100 motorcycle that came with bias-ply tires?

You should usually stick with what the bike came with originally. Although radials have numerous advantages, the bias ply tend to have more rigid sidewalls, and with the weight of your bike, you might need the rigidity, less you get a slightly squirly situation. You might not get the great lean angles that bikes equipped with radials get due to the contact patch and traction, but bikes equipped with radials have these excessive lean angles planned during design and construction. Whatever you do DON'T MIX BIAS WITH RADIALS. you've got two tires with different characteristics, and every manufacturer will say it's iffy at best. Many manufacturers have great bias and radial tires, and your best bet is, you get what you pay for with tires. If you equip cheap tires your tires will transmit this to you, if you put more premium grade tires, you'll have a better ride. Keep your tire pressure up, if you're running 20lbs like these wannabe rossi's are trying to do on their cheng shins and F2's you're gonna get into an accident. Keep it up, especially on a touring bike, I run 38-40 in front and 40 rear, hot, cold, fast, slow, my tires last a while, the bike handles crisp, and I have never had a problem with traction in any situation that didn't deal with my own miscalculations. Yes, I've ridden Rain, Snow, Sleet, Shine and 115 degree days. Other than keeping good tires, work on being smooth, smooth is fast and fast is smooth.