Check air pressures.
Check your head bearing nuts are tight. There should be some slight resistance when the bars are turned from side to side with the wheel off the ground.
Check the torque on all the front and rear suspension bolts.
Also, check and set suspension sag. If the rear is too soft, it will cause head shake so bad that it can lead to a full on tank slapper.
Your rims could be warped or not centers around the hub. That would be felt as a bounce. Vids on youtube showing how to check and true a spoked wheel.
It's not uncommon to find a tire that is out of round or has a bad section. That would require a tire change but not to expensive on the RX3.
Check that the rear wheel is aligned. I measure between the axle bolt centers and the swing arm bolt centers. I also use a motion pro tool on some of my bikes. It's cheap quick and accurate. Links below.
https://www.amazon.com/Motion-Pro-08...language=en_US
Videos of alignment tool.
https://www.youtube.com/results?sear...alignment+tool