I just re-checked the datasheet of this sensor: https://cdn-shop.adafruit.com/datasheets/BST-BMP280-DS001-11.pdf
You should be able to use yours in either I2C or SPI mode. So SPI mode should also work, provided that you've made the right connections, AND you make sure that the interface selection procedure on startup involving the CSB pin is performed correctly. See section 5.1 on page 28 of the datasheet. You'd have to check the Adafruit library if this indeed performs the correct sequence.
Consult the Adafruit examples/tutorials through this page: Overview | Adafruit BMP280 Barometric Pressure + Temperature Sensor Breakout | Adafruit Learning System