Can one follow Hinduism and Buddhism at the same time?
In Buddhism the main teachings you have to have faith in is the 8 Fold Path divided into 3 trainings, which is to develop higher virtue, higher mind and higher wisdom.

No religion is incompatible with developing higher virtue, higher mind and higher wisdom, therefore you can start practicing considering you self a Hindu. As you find parts of Buddhism logical and verified at the experiential level then you can lowly accepting parts of Buddhism at your own pace.