Can I put game fish in a 5-gallon bucket with water and transport them live?

No; only legal bait and legal live baitfish can be transported in water. Since fathead minnows, sticklebacks, and creek chubs remain as a legal live baitfish, there is no alternative other than to allow some water, in bait buckets, to transport minnows to a water body for fishing. In the case of game fish, there are viable alternatives to transport them home or to a fish cleaning station, and they do not need to remain alive.