私は毎日大学にバスと地下鉄で行く。Езжу на автобусе и метро. (всегда оба) 私は毎日大学にバスや地下鉄で行く。Езжу на автобусе, там, на метро.. 私は毎日大学にバスか地下鉄で行く。Езжу на автобусе или на метро. Примерно.

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.