私は毎日大学にバスと地下鉄で行く。
--> You always get on both of them, bus and metro/subway. Two of them are necessary for you.
私は毎日大学にバスや地下鉄で行く。
--> There are cases you use both of them, one of them or other transportation, for example, by bicycle.
私は毎日大学にバスか地下鉄で行く。
--> You always get on one of them. You need to use bus or metro/subway, but not both of them. Besides you don't have other options.
I hope this was helpful.