Bux. was totally loyal to the IF, and there is no real evidence to believe otherwise. She was released by the Bolsheviks along with Gilliard and Gibbes because they believed from her name that she was German, not Russian. I did rather a lot of research into the basis for the claims that Bux. betrayed the family, and the evidence turned out to have been made up by a Bolshevik sleazebag, who was married to Rasputin's daughter, and acting as a double agent, collecting funds from the loyalists to the Regime, pocketing the money then turning in anyone trying to help Nicholas to the Bolsheviks.
Anna Vyroubova sent a large sum of money to Ekaterinburg, which she raised in Petrograd, to support the IF. The double agent recieved the money, then "said" he gave it to Bux. She of course never got it. It was his lie that people were using to believe she betrayed the IF. The truth is that she didn't betray them ever.