If you want to present a peace offering from the herd, use either a bull or a cow.
In the Old Testament worship of Israel there were several sacrifices. They were the constant reminders of two great truths that are still of vital importance today. One is that God is holy and separate from all that is sinful. The other is that we are not holy and we can only have fellowship with God when he shows us how to have fellowship with him and provides the way for this to happen. The different types of sacrifices in the Old Testament religion showed the different aspects of God's way of salvation, and so to fellowship with him.
One of the sacrifices was called the Peace Offering — the word "peace" is the word "shalom" that many people today use as a greeting . This "Shalom" offering was use for several reasons, one of which was as a way of expressing to God a big "thank you" for all the blessings that a person had experienced, and he wanted God to know how much he appreciated them all.
This offering is often linked to the blessings we now have through the Lord's Supper and the sacrifice of the Lord Jesus which it represents. This is often spoken of as the cup of thanksgiving — saying "thank you" to God for his way of salvation through Christ Jesus. This brings us "shalom" indeed, and fellowship with him.
Dear Lord Jesus Christ, we thank you for your sacrifice for us and pray that we never forget how great a debt we owe to you for this. Amen