In principle, you could put the whole thing in a box and send it up on the shuttle, park it on ISS and bring it back when done.

Trouble is, the whole thing has to be safety tested for a manned environment which adds so much delay and cost it makes the whole thing pointless, or nearly so.

If they can get a free launch on the Shuttle, it would be worthwhile.

Personally, I'd be knocking on the door of the Russians and asking them to take something up on a Soyuz.

Full Mars society release below:

Mars Society Launches Translife Mission Project

At its Stanford convention, the Mars Society resolved to commit its
resources to initiate the Translife Mission as its first spaceflight
mission project. The Translife mission will consist of a Mars-level
(0.38 g)artificial gravity spacecraft carrying a crew of mice (and
possibly other animals and plants) in low Earth orbit for a period of
roughly two months. During this period, the mice will be allowed to
reproduce and the young will develop into adults. The spacecraft will
then be brought down to Earth, and both the original crew and their
progeny will be examined.

The mission will:

1. Validate the miniature artificial-gravity spacecraft and life
support system for further missions.

2. Establish whether Mars-level artificial gravity can serve as an
effective countermeasure for mammals against the physiological
deterioration that accompanies long-duration spaceflight in zero
gravity. Answering this question is key for planning human
expeditions to the Red Planet.

3. Establish whether mammals from Earth can be born and develop into
proper adults in Mars gravity conditions. Answering this question is
key to establishing whether humans and other life from Earth can
ultimately settle Mars, and by implication, other planets with
gravity substantially less than that of the Earth.

Follow-on missions could include flights into deep space, possibly as
far as the orbit of Mars.

Individuals or organizations willing to volunteer talent, hardware,
or cash in support of the Translife mission should write the
Translife Project, Mars Society, Box 273, Indian Hills, CO 80454. All
donations are tax deductible.