Panniers perhaps combined with a box, would be my method of choice, I think.

I've been picking up flowers for my wife the last several months. It's winter here, and it has been around freezing for a few of the runs.

I have a burley travoy, and I put an insulated backpack on it, so the temps aren't too aggressive. But I have this special insulated mug that transfers the heat of what's inside (hot or cold) when shaken, so I wrap it up and put hot water in it, and it keeps the inside of the cooler nice and warm. 😁

The last plant in picked up was small enough to put in a pannier with that water bottle, and then I rode back home approx 20km. No issues at all.

Sometimes I can get away with a front basket with an insulated insert.

There are so many ways to do it, but it can depend on what equipment you have on hand.

At the store get a couple extra pieces of the wrapping paper to cover it. Wrap the outer layers loose, so they take the pressure and prevent the flowers from getting squished. In a pannier or backpack they can stick out, but they should be fine as long as the paper doesn't get wet.

Source: I've carried bouquets on buses, in panniers, and on foot in Ottawa winters.

In my teeth

wrap in cheesecloth or a tea towel and straps just the stems to a rear rack with the stems pointing in the direction of travel