Information on the Find a Grave website states that James came to America in 1861. The only James Bowman I have been able to find on a ship manifest in 1861 was born about 1821, and he came to America alone on the Monarch of the Sea. This may or may not be James.
His name does not appear on the 1856 Utah census. The first documentation to place him in Utah is his association with the Morrisite church in June 1862, which was prior to the arrival of that season's emigration. In the Spring of 1863, he moved to Idaho.
His wife, Isabella, was killed during the Morrisite War 13 June 1862 at Kington Fort, Weber County, Utah.
Further research is needed to determine the name of the pioneer company that they traveled to Utah with.