If you missed the last shuttle, or if you just missed one and don't fancy waiting 25 minutes, buses 175, 188 and N32 (providing 30-min service all night) can also bring you to the hotel. It's 4 stops then you will need to cross a big intersection diagonally.
Most buses have ticket machines in the back, it's an honour system and you board by the back doors (not sure if night buses are different). If you don't need a 24-hour ticket then it's PLN 3.40 to the hotel (less than $1/€1/£1)
I did use the 175 bus to get into the Old Town and back. The ticket machine on the first bus was not very responsive and I had to try contactless as well as PIN before it spat out a ticket. The second ticket machine was more responsive. I see two transactions of £0.89 each on my credit card statement, so it must have worked ok.