Some bugs have internal fluids that are similar to lacquer, some are acidic. If they stay on too long, they'll mark your paint & no amount of scrubbing or chemicals will remove the marks. I'd suggest a 3" orbital buffer and a good polish. I use Griot's products, so I'd start with the #3 polish. If that doesn't do it, go to #2. Don't use the same pad. If you go to #2, finish up with #3. Plan on this taking some time. I had a bug spot on my fender that I missed cleaning off after a ride - I worked on the spot with #3 for an hour to get it off. Griot's makes a #4, but is is so mild, it has almost no "cut."
I always wipe my bike down within a day after a ride with Griot's Speed Shine and a micro fiber cloth. Harley's bug remover also does a good job of loosening bugs and it's safe for windshields.