If your plant is outside, it might be difficult to keep the soil at the proper moisture level being that the pot size is only 4".
I would recommend a 2 gallon size pot at least for best growth potential. Don't use a clay pot as these have a tendancy to dry out at the root level too quickly.
Your plant will increase in size depending on the amount of roots the plant has.
Hope this is helpful.
Meg

Excellent response from Meg.
The mini will definitely get bigger and bushier given more room to grow. Generally they are already very rootbound in their 4" pots. The bush will probably be anywhere from 1'x1' mature to 3'x3' depending on the exact variety and the zone you are in. Exact variety is generally hard to discover if you purchased it from a box store as a Parade or other 'grocery store' mini.

If you have the rose indoors, get it outside pronto as they just aren't houseplants.

Suz