Professor Slughorn was never willingly going to follow Tom. He hadn't said as much, but it was there in his eyes this disgust at the mention of his name. Bellatrix just didn't know how she was going to explain this to Tom she couldn't let him know she was failing.
Everything would be a lot simpler if her head of house would just join Tom. Why couldn't he understand that Tom was the future of the wizarding world.
That he was going to build a world free of Mudbloods. The fact the head of Slytherin didn't want that made her feel sick, he was a disgrace to her house and more importantly he was against Tom's belief.
She was also pretty certain that Slughorn had spilled that fact, she had several times attempted to recruit him to Dumbledore. If Dumbledore knew then things were going to become extremely difficult for her at Hogwarts.
She would be watched all the time and that would make hard to complete her mission.
Bellatrix was beginning to think the only real choice she had was to admit she was failing to Tom and see what he advised her to do.