You can usually walk after having bunion surgery but it might be painful for a bit as you recover from the bunion surgery.
You might also need the assistance of a crush or cane at least for awhile when walking after you have the bunion surgery done.
You will usually also wear a special surgical shoe to help to keep the weight on the heel or outer edge of your foot until you recover fully.
The recovery usually happens pretty quick though and soon enough you'll be able to walk again without assistance and pain.