Starters ...
Quick answer - I am not aware of any cards or special bus concessions for guests from Ukraine, apart from one offer of free travel to reach your host when you arrive, from First Bus who operate the D1 service from Bath through to Warminster. In practical terms, I have not yet heard of anyone using this as most guests are being met by their hosts at airports or major rail stations and not being left to find their own way by bus to the place they'll be staying. There is a similar "get you there" by train scheme if you have proof of arival within 48 hours.
I do a lot of public transport work and am addressing the issue in a discussion at
http://www.passenger.chat/26342 . There are twelve different bus opeators (at the last count) in Wiltshire, and each has there own fare system, special offers, and each is a company who are - in nearly every case - responible to their owners to make a profit or at least break even. Subsidies and grants help keep services running and provide some regulation of fares but, yes,
UK▸ fares tend to be expensive compared to other countries and I don't have an easy answer. I am speaking to Wiltshire Council tomorrow and I will ask if there are any county-wide opportunities. In reallity, I'm expecting that apart from a few "headliners" such as the First Bus one which provides them with great publicity and almost zero cost, there will be little "special". I could be wrong, and after speaking with County I may approach bus companies and explain to them that a concession for a month would help their business in the future by getting people onto the buses and it becoming a way of daily life.