How can I buy and use an one-day bus ticket in Tartu, if that is an option?
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I found this on the contactless bank cards FAQ:
Which tickets can be bought?
One can only buy an hourly Tartu ticket (0,83 €) with a contactless bank card, one cannot buy a discount hourly ticket. When you buy three or more hourly tickets during one day, the hourly tickets are automatically replaced with a one day ticket (€ 2.11).
(italics added for emphasis on the relevant part)
So if you are using a contactless card, then to buy a day ticket you simply buy a single ticket for each trip you take. When the total cost of the single tickets exceeds the cost of the day ticket, they are automatically replaced with a day ticket.
I would imagine the same applies if you are using the bus card, although I haven't found any explicit confirmation of that.