"A son of a wealthy sheikh goes to Germany to study university and broaden his horizons in a new culture. His father sends him a letter, asking him how is it going there. The son responds:
"Everything is great father, although I feel a bit inappropriate - I am the only one driving to school in my car, everyone else is using the bus."
The next day he wakes up, gets ready for school, goes to his parking spot and there is a huge new bus standing there, with a note from his father that reads:
"I don't want you to put our family in shame. Here's your new bus."
Click on "Tips and Notes" in earlier lesson on colors for explanation of weak, strong and mixed adjective endings, plus tables of endings for each type.
You can also find a good explanation along with a very simple and very helpful flowchart at this site:
Let's break it down. First, you're right that Bus is masculine and in the accusative, that affects the preceding words.
"sein" is a possessive determiner. When learning German it's good to think of possessive determiners as in the same group as the indefinite article "ein". Possessive determiners are conjugated the same way as the indefinite article and they have the same effect on adjectives that follow them. -en is the masculine accusative ending for indefinite articles/possessive determiners.
When an adjective follows an indefinite article/possessive determiner it has the mixed inflection and the mixed inflection masculine accusative adjective ending is -en.
Mr.rM's comment above links to the inflection tables. There is a logic to all of this that you gradually learn but it takes awhile.
Because Bus is masculine and accusative, sein needs the -en suffix/declension.
Because Bus ist Akkusativ there needs to be some indicator of case, and that is accomplished by sein
Because seinen has provided the case indication, eigen needs either -e or -en as a suffix. We choose -en because case has changed. (This gets to the "big three get an -e" rule that Jess1caMar1e has provided in previous posts.)
Unfortunately, I can never remember if that's weak, strong, or indifferent inflection.