I want to know if one can bend a note and simultaneously use throat vibrato on the note. I can use these techniques independently but when I try to vibrato the bent note I lose the bend.
Yes, you can. The *sound* of the vibrato tends to change from a variation in the pitch to more of a pulsation in amplitude, but it's a common enough usage. The fact that you're losing it means you either need more control over your bending, or need to relocate your throat vibrato a little - it should come from a glottal contraction, the same as if you were coughing.
Listening to Howard Levy in this regard is interesting. He uses a lot of deep bends on the low notes, and tends to use tongue vibrato to subtly modulate the pitch of the bend instead of throat vibrato for these notes, as it is better suited to his style.
