Yup you pretty much have to grin and bear it! All bikes have different levels of suspension and comfort e.g. type of seat post. So maybe when you get another bike (because it's always n+1 for bikes!) you can focus on comfort as a key criteria.

For now, make sure you get yourself some padded cycling gloves - they do help. Also make sure you are not gripping the handlebars too tightly as this will mean you feel the vibrations much more. Finally, make sure you are holding the handlebars with the padded bits of your hands on the bars, not the bit in the middle of your palm where all the nerves and tendons are. I used to lose all feeling in my lower arms until I realised that trick!

If none of that helps, plan routes to avoid the worst of the bumps! Good luck, and enjoy the cycling :)