I see where you are coming from that question. Natural products are one of the most researched areas in chemistry that deals with the usage of plant extracts to test for properties, in your case, anti-asthmatic properties.
There are methods that are necessary actions to put the animals in certain bronchospasm condition. It would be better to use larger animals (although mice can be used as well); guinea pig is a better option. Fasted guinea pigs are then exposed to histamine aerosol (~0.2%) produces by a sound nebulizer in an aerosol chamber. Physical manifestation such as pre-convulsive dyspnoea caused by histamine should be monitored because you will start from that point. Just be sure that you let the guinea pigs/mice alive because you will have to let them breathe in fresh air again and then induce your plant samples.