You are correct that M81 transits the meridian at upper culmination just past mid-February in the eastern US. As long as the Moon is well below the horizon, as it will be in Feb. 2020, this will be the best time to observe M81, and its neighbor, M82. Since these galaxies are relatively bright, good views are available from late December through early May when they are 40+ degrees above the horizon, as long as, there is no interference from the Moon. I have taken some of my best photos of M81 & M82 in March and April, mainly because they are a bit farther to the W, avoiding some local light pollution here towards the NE.
It's likely that many think early Spring is the best time to observe M81, since they don't have to stay up so late; in the eastern US, M81 transits the meridian about 10 pm in mid-March and 9 pm in early April.
Edit: Added answer to question from the comments.
The simplest and most accurate way to determine when an object transits the meridian at your location is to use astronomy software such as, SkySafari, Stellarium, Cartes du Ceil, or any of the many other planetarium type programs. However, I started amateur astronomy many years before smartphones, tablets, gps, and even personal computers. So I learned to estimate when objects in the sky would be visible.
At my location, around 10 degrees of longitude to the east of yours, I remember that the meridian on January 15th corresponds to about 8 hours of right ascension. Since the sidereal day is about 4 minutes shorter than the solar day, RA at the same location and time increases about one hour in 15 days, or about 2 hours per month. Precession changes this RA slowly over time, however, it is a useful approximation that is roughly valid over decades.
Thus, M81 at 9h 56m RA, will transit my meridian near midnight around Feb 15th, and at your location a few days later. A month later M81 will be two hours farther to the west, so will cross the meridian earlier, around 10 pm.