If you have full stuffed bag full of laundry with two handles, how would you tie the handles?
Fold each handle into itself and treat each as a single strand. Then just tie those two strands together in an ordinary square knot.
Here is an example showing a similar bag, although much smaller and with shorter handles. The photos show things step by step: 1) pull the handles out into two doubled-over strands 2) right over left and under 3) left over right and under.