Hi There!
I add you the time of the different transportations, so it's easier to get an itinerary in mind.
Bogota - Villa de Leyva: around 4 hours - You're right to sleep 2 nights, so you have time to enjoy the town. It's a lovely place!
Villa de Leyva - San Gil: Around 4 hours then it's 30 min to get to Barichara - But you have to change bus terminal - You have to go to El Terminalito
Barichara is lovely and 1 night is enough to appreciate the area
It took us 14 hours with the night bus to make San Gil - Santa Marta. In Santa Marta, you need to get to another "terminalito" to go to Tayrona, and then it's 1-hour bus drive. After all these buses, I think you won't want to hike in Tayrona ;) - Enjoy the afternoon in a nice hostel/hotel around the Park (The journey, Yuluka hostal, Villa Maria, etc.).
By doing that, you can let your big backpack at the hotel and you can start early your hike the next morning - It's more pleasant you will see ;)- You should read this article to know everything about Tayrona ^^ https://www.tomplanmytrip.com/tayrona-colombia-a-massive-and-unforgettable-park-all-secrets-revealed/
You can decide to sleep 1 night + staying late the next day then sleeping another night at the hotel near the entrance.
Or you sleep 2 nights in the park and leave early the next morning - Don't forget your backpack at your hotel ;)
Then you can sleep 2 nights in Minca - It will take 2-3 hours from Tayrona
https://www.tomplanmytrip.com/casa-elemento-casa-loma-detailed-guide-know-everything-need-minca/
Minca - Cartagena: It's almost a day trip. You should count 5-6 hours with a private shuttle (Check Marsol facebook page) and around 7-8 hours with public buses.
You spend 2 nights in Cartagena
https://www.tomplanmytrip.com/step-by-step-guide-visit-cartagena-de-indias-48-hours/
Then you fly to Leticia
Day 1- Arrive in Bogota
Day 2- Bus to Villa de Levya
Day 3- Villa de Levya
Day 4- Bus to Barichara
Day 5- Barichara, then overnight bus from San Gil to Santa Marta
Days 6: Hotel near the entrance to the park
Days 7: Tayrona
Days 8: Tayrona
Day 9: Direction Minca
Days 10: Minca
Days 11: Bus to Cartagena
Days 12: Cartagena
Day 13- Fly to Leticia, transport to Reserva Natura Palmari
Days 14-16- Reserva Natura Palmari
Day 17- Fly from Leticia to Bogota
Day 18- Depart Bogota