I think your real issue isn't so much the Blue Lagoon back to Reykjavik part but from the BSI bus terminal to the cruise port part. Based on your information, it seems you have about 30 minutes to do this (assuming that "all-aboard" time is 1:30 p.m. of course).
Do you know which port you'll be docked at? Reykjavik has two (at least?).
The city centre's not that big so if worst comes to worst, when you arrive at the BSI bus terminal you could probably take an expensive taxi ride to the port instead of a transfer bus to the port which might take a more scenic route than you'd like. According to Google Maps, the drive should not take more than 15 minutes to the probable port (you will need to confirm which port it is for your actual ship/sailing), so it appears do-able (with a taxi fare backstop) but cutting it close:
https://www.google.ca/maps/dir/Reykjavik+BSI+Bus+Terminal,+ReykjavÃk,+Iceland/Reykjavik+Cruise+Terminal/@64.1446302,-21.9150262,14z/data=!3m1!4b1!4m14!4m13!1m5!1m1!1s0x48d60b350153a4cd:0xc33373e2c14646c7!2m2!1d-21.9310479!2d64.1375715!1m5!1m1!1s0x48d675d9647292ed:0xe72d3270593c9ac8!2m2!1d-21.861768!2d64.1555!3e0
The other issue as the poster above mentioned is how sure are you that the ship is leaving at 2:00 p.m. If closer in to the date of actually arriving at the port the departure time changes to an earlier time, will you be able to adjust accordingly? I found this from the Blue Lagoon website ( https://www.bluelagoon.com/legal/blue-lagoon-terms-and-cancellation-policy😞
"FOR BOOKINGS TO THE BLUE LAGOON AND RETREAT SPA FROM JANUARY 1st, 2022 UNTIL DECEMBER 31st, 2022
- If you cancel with more than 48 hours notice: 100 % is refunded
- If you modify your booking with less than 48 hours notice, we charge you an extra fee of ISK 1800
- If you cancel with less than 48 hours’ notice: No refund is made
Blue Lagoon Ltd. reserves the right to cancel all bookings and reservations, when unable to provide the company’s services due to Force majeure event, such as but not limited to weather, strikes, natural disasters, or any other irregularity outside the company’s control. In such an event, no compensation or refund is payable."