Yes, the new law includes anyone riding a bicycle as well as those driving a motor vehicle.
For the most part the new law restricts the use of handheld communication devices for any reason while driving. There are some very minor exceptions, however, noted here:
If you are reporting a health, fire, safety or police emergency you are able to make a phone call while driving. But, if you are stopped by a public safety officer for making the call and are cited, you may be asked to verify that an emergency call was made in court. The ordinance does not apply to governmental fire agencies, law enforcement agencies, emergency responders and other authorized emergency vehicles.
The state of Montana does not have a state wide ban on the use of handheld devices. State legislators there believe the issue is best left to municipalities to determine what is right for their community. Obviously the community leaders of Great Falls believed the issue of distracted driving caused by the use of handheld devices was great enough to warrant a comprehensive ban on their use.
Police in Great Falls have been authorized to make stops of vehicles they see where the driver is using a handheld communication device, but they will not investigation called-in reports of the same. In other words, they must see the infraction taking place before being able to do anything about it.