Can I close shave 12 months after beard FUE or will I have permanent bumps/small scars on my face?

It's great that you're considering all aspects of beard FUE before going forward. Beard FUE typically leaves very small, dot-like scars where the grafts are taken and implanted. These scars are usually minimal, especially when the procedure is done by an experienced surgeon. However, if you plan to keep your beard at a clean-shaven level or close to a 5 o'clock shadow, these small scars may be more noticeable compared to someone who keeps a longer beard.
At 12 months post-op, your skin should be fully healed, but there is always a chance of subtle texture changes, like slight bumps or small scars, especially in the donor area or where grafts were placed. That said, many patients can still clean shave without noticeable issues, especially if the scars are tiny.
If minimizing scarring is a priority for you, it's essential to discuss your goals with your surgeon beforehand and ensure that they use the smallest punch size possible. Also, keep in mind that everyone's skin heals differently, so while some people may experience more visible scars or bumps, others may heal with almost no noticeable marks.
In general, though, most patients are happy with their results and can alternate between a clean-shaven look and a stubbled beard without significant issues.