10 minutes of bridging can only make your neck stronger so why not?
As far as a routine goes, perhaps you could add in head raises.
We do 3 different exercises sometimes during warm-ups and they suck. You lay flat on your back and then lift your chin towards your chest and then back. Do not allow your head to rest on the ground between reps if you can help it. Do 50 of those - chin to chest.
Then still on your back with your head off the mat, do 50 side to side ear-to-shoulder touches. Touch your left ear to your left shoulder and then your right ear to right shoulder, that's 1 rep.
Lastly, touch your chin to each shoulder, twisting your neck, still with your head off the mat. Chin to the left, chin to the right = 1 rep. 50 of those.
If you aren't gritting your teeth by then or haven't rested your head, you are tougher than me. You also may want to do more of them.