Transportation between Russia and Ukraine

First of all, youu need to know that direct flights between two states are canceled, so if you want to fly from or to Moscow, you need a stop in some other country, for example, Belarus (most popular option is Minsk).

Now, back to your options. If you want to catch up a train, you need a layover, either in Moscow (which is very time and money consuming tickets), or in Bryansk (train schedule available on tutu). All in all, your trip would be near 70 USD from Voronezh to Kiiv, and after that you need to use either a bus or train to Kropyvnytskyi (new official name of Kirovograd), so the trip would be over 100 USD in one way.

If you need some cheaper option, the bus is for you: you can get from Voronezh to Dnipro (new official name of Dnepropetrovsk) by bus for 20 USD (tickets can be bought here, for example), and from there to your destination by bus for near 8 USD (sample tickets here).

Please note that for Russian women it's recommended to have an invitation to Ukraine from somebody from there, and for Russian men in age from 16 to 60 it is mandatory to have one.

While the above answer is completely adequate, I wanna also propose you the Blablacar option, which is definitely more handy comparing to buses and train layovers, and of course exponentially cheaper than planes.

While direct rides to Kropivnitskiy are rather rare, they do exist and it is worth to check for them periodically.

More realistic option, however, is to ride to cities-satellites or nearby cities, from where you can easily get to Kropivnitskiy:

1. Krivoy Rog. More than 100 rides on Blablacar for now.
2. Kremenchug. Also very popular destination.
3. Oleksandriya