Time frame from bug bite to get cellulitis?

Variable : A skin reaction from an insect bite is most often histamine release by your own immune system causing mild redness, swelling and itching. Cellulitis infection is less common and and typically much more intensely red and painful and often increases in size. It could develop anywhere from 24 hours to days later.

Could be quick: If you have immune compromise it could be hours, if not it might take a day or two. Immune compromise can be from diabetes mellitus, cancer or if you've received an organ donation and take suppressive drugs. Those taking Prednisone or rheumatoid arthritis medications can also catch infections easily.