Try turning the pipette a few time. Almost a twist motion. That has been suggested to me in the past.

When a friend taught me how to AI she suggested that I put my finger in first and then guide the pipette along my finger to position it properly.

But your finger only goes a short way in. I go up, over the pelvic bone there, then straight towards the head. If I encounter resistance, I'll pull it back a bit and try again, gently. I also turn it a bit. I will usually pull it back a fraction before putting the semen in so that the end of the tip is not right up against some tissue and the semen can come out the end easily.

2 Suggestions -
First - I love the M-2-Blue Insemination Tube, 10 inch with Adapter - Indiv. Wrapped and Sterilized.
http://www.reproductionresources.com/products.php?pid=650&detail=true

They are much thinner but never kink. The stainless rounded tip slides in without getting hung up on folds. The semen comes out the sides so no problem if the end is up against tissue.

Second - I also prefer to inseminated bitches lying down.I lay them down preferably on their back in an OFA position with their legs straight out and I rub their tummy. When they are in this position and they are relaxed, the pipette slides straight in. You don't have to go up and over anything.
If your bitch won't lie on her back, lay her on her right side, if you are right handed, use your knees to push her knees and legs straight out behind her and you can accomplish pretty close to the same straight alignment where the tube has a straight path to travel.

Once you are finished inseminating, remove the pipette and I sit on the floor with my legs straight out. I leave the bitch on her back between my legs with her rear raised up in my lap, up against my chest and her rear feet pushed up to her chest. (Picture a woman on her back with her hips raised and her knees up to her chest.) This allows the semen and gravity to do their job. I also massage the bitch's vulva in this position.

I've never heard of a doctor asking a woman to stand on her head after an artificial insemination :o)
I've also seem too many people hold the bitches with their waist up over the person's knees blocking the flow rather than assisting it.

I've never heard of a bitch showing discomfort when the AI tube was in the bladder.

To avoid this possibility - use just the AI tube until it's placed properly - then attach the syringe with the semen in it. If you do place it in the bladder you'll know right away as the urine will come flowing out. Not able to notice this when the semen syringe is attached before placing the AI rod. If you hit the bladder instead - just make sure to change the rod to a new one.

With those larger insemination rods, I would think it would be impossible to hit the bladder. The opening to the bladder lies on the floor of the vaginal vault and is almost impossible to catheterize if you wanted to!! I use the polypropylene urinary catheters which were shown to me by one of my mentors in the breed (NHL you taught me well!) because they are more flexible and less traumatic and painful to the bitch. They do seem to accept it better, and barely notice it's presence.
I have accidentally catheterized the bladder three times in 22 years, much to my surprise! If the syringe with the semen is connected to the catheter, I always draw with the syringe to pull urine into the catheter if I accidentally hit the bladder. In this case I would pull it out, get rid of the urine, and start over again.

Do you have photos of this technique? This sounds interesting and I'd like to learn more.

duckndogs@telus.net