Giant Pok Hi,
Sorry, but your Swiss Travel Pass is not valid one day earlier, you have to buy a full fare ticket. It is not necessary to make a seat reservation. You can also buy such tickets at the airport station after your arrival (vending machines or ticket office).
You also have Supersaver tickets valid only in the selected train, but it is not recommended to buy such tickets because you don’t know it your flight will arrive on time in Geneva. If you are late and miss the train, you must buy a new ticket.
You don’t have other alternative from Geneva to Bern, long-distance buses are only available for international trips in Switzerland.