She can text him once a week to keep him her informed of her progress throughout the pregnancy. If she does it too often, he might leave town or change his phone number.
If she wants him to stick around in her life, she can write little compliments to him about what she enjoyed about knowing him. These show she holds him in high regard, but is not applying pressure to saddle him with child support payments.
From time to time, give a longer break between the texts, like 2-3 weeks so it becomes a surprise that she is still thinking about him even though she is getting on with her life.
You should be saving some EXTRA money towards the child's future. This shows your wife that you are happy and supportive of one extra in the family. You need to do more chores and give some thought to getting the baby's room ready.
Fresh paint and wallpapering, anything that shows you are getting excited about your new responsibilities as a father or step-father. You made a joint decision for her to be bred, so let yourself feel like a celebration is in order. You need to clink the glasses, you have struck gold.
You saved a lot of money by not having to go to a sperm bank to buy sperm.
Collect photo ID, tax numbers, names of siblings, and other information so that the child can easily track down it's biological Father later on in life. Don't pressure the Father, but make it possible for the child to find him.
The real bull may secretly watch while you and your wife and HIS baby go down the street. Let him feel he can come and see his child anytime he wishes, because this will make it so much easier for the child to make contact with the father when it gets older.
Your wife can text the Father on important occasions, like birthdays, going to school, learning to walk, ride a bike, to keep Dad gently in the picture. Photos sent can be helpful.
If appropriate, a hubby can make up albums of the baby's first years and post them to the biological Father, so the photos are printed in his brain. This will depend on whether this is going to cause awkwardness for the bull with any other relationships he has.