“Whoever solicits or receives any .thing of value, in consideration of the promise of support or use of influence in obtaining for any person any appointive office or place under the United States, shall be fined under this title or imprisoned not more than one year, or both.” — 18 USC Sec. 211 — Bribery, Graft and Conflicts of Interest: Acceptance or solicitation to obtain appointive public office
...in consideration of the promise of support or use of influence in obtaining for any person any appointive office or place under the United States...
The state of "not being an elected official" does not constitute "promise of support or use of influence."
Basically, you offer Joe Blow the job of Chief Assistant Undersecretary of Agriculture. He can't be CAU of A and a senator at the same time, so if he takes the federal job he won't be a senator. That's what's going on.
Is it ethical? Probably not. Does it constitute bribery under the federal statute? Again, probably not.