Yes, burying Beatrix with a knife and flashlight would have just re-assured him that he is not that same ‘mean old bastard’. He wants to get away from that life, and by killing Beatrix directly he is basically just playing his Sidewinder part again, which he doesn’t want to do. But how did Beatrix know of the knife in her boot? Did she know Budd put it there on purpose? in which case if Beatrix did escape she would have spared Budd, killed Elle and Budd could go on living how he’d like, otherwise he would have got away anyway maybe.
She probably just felt it in her boot, but I’m not sure if she knew or not if Budd put it there on purpose. But I never really thought about whether she would have spared Budd or not. She did basically “spare” Elle, so she may have done the same with Budd. But we’ll never know for sure since Budd was already dead by the time Bea got to his trailer.