Grapes can stay out at room temperature as long as they're being eaten that same day.
If you don't plan to eat the grapes in that same day then you have to refrigerate the grapes to keep them cold so that bacteria won't grow on them.
Grapes must always be refrigerated and kept cold when not being eaten.
Leaving grapes out at room temperature without refrigeration for longer than a day can cause mold to grow on them and be sure to inspect the grapes for any mold and if you see mold on some grapes remove the grapes from the bag and throw them away but you can refrigerate the good ones.
Grapes are also highly perishable and do not ripen once picked so always refrigerate them in a perforated bag to keep them from spoiling when not eating them.