not only new mattress, but clean all bedding thoroughly as well.
clothes and furniture may also be conduits for bed bugs so you will have to completely wash/fumigate everything that is fabric at a high temperature.
if it is not your home that is infested, you may have also carried them to your home on your clothes.
the bedroom should receive a complete clean-out to kill everything
If you have bugs on bed, they moved to your clothes also.
Once, you changed mattress and washed bed sheets, you should do the same with EVERY piece of garment you have, in other words 'Everything cotton-y must go to the washing machine.
'Bastards, they spread fast .....'