One way is to make one opc tag per integer and define an alarm per bit on each integer tag. This is a pretty common way of storing/configuring alarm information.
You could also go the route you are thinking and make a tag per bit, which helps with visualization and configuration(one alarm per tag instead of 16 alarms per tag)
If you have a large number of tags to set up, you can utilize system.tag.configure to script the creation of the tags all at once. This post has some decent information on how to achieve this.
Pturmel also has his Spreadsheet Import Tool that may be of use if you're not as script savvy.