It's not the saddle that tilts but the bit of the seatpost that the saddle attaches to...so a new saddle won't help. Post a picture of the seatpost fixings with the saddle removed
If anything, you might need a new seatpost if there really is no adjustment! Or take the bike back to the shop and ask them to take look
If the saddle feels hard, you may just need to toughen your derriere up by more riding if new to cycling or perhaps try different shorts...if you're riding on a turbo (for an hour zzzz), you will need to move around a bit, stand up, all the things that you would do on the road ... and which help to relieve bum ache