The train from Cologne to Brühl is maybe 4 euros (maximum) each way, and then 3 euros return for the shuttle bus, so to travel in and out of cologne each day would cost you 11 euros return. However, I personally wouldn't suggest this unless you are planning on doing extensive sight seeing in cologne (which there isn't much of; the chocolate museum and the cathedral are the only two main draws IMO).
The "Six!" Boutique hotel is located in the centre of Brühl and near to lots of supermarkets, clothes shops, bakeries, and restaurants (which would give you plenty of dinner options as the park closes before dinner time really, unless you want to eat in the park hotels, however that's quite expensive). The six hotel is a 5 min walk from brühl train station where the shuttle bus departs from.
The hotel h+ (from researching now) is a 25min walk from Brühl train station and then you can ride the 985 bus from the hotel to the park which takes under 10 minutes. Theres also a bus connection from the train station to the hotel but still requires 10 or so minutes of walking out of your way to the hotel. H+ would likely be equipped with its own onsite restaurant etc.
Your other choices are looking on booking.com to see if there are any other good value hotels in Brühl town centre, but from my research I didn't really find anything stand out. There are often lots of cheap Airbnbs available around Brühl near to the train station, and hence the shuttle bus, which you could look at renting out for a cheaper price than a hotel.