When you are describing the "action" of fastening a bike to a tree or fence in English, we usually use the phrase of "locking it up" "I am going to lock my bike up, to that tree." "I have just locked my bicycle to that post over there." "I secured my bicycle to that post with a lock and a chain." Informally,..we might use a word like "fastened or hitched" "I hitched my dog and bike to the same tree." Hitched or fastened when used would come across as improper grammar, but still would be descriptively accurate...but in English the words locked up or secured or chained up would be more preferred to describe the action of "fastening a bike". As for dogs, livestock such as cows and pigs are usually described as being "tied up" because they are living creatures and bicycles are machines. For most sentences this is the easier way to think of it. When we fasten an animal to a tree or post with a leash or rope. We might say something like.. "I tied my pet dog to that tree next to where I locked up my bicycle." "My dog is tied to that post beside my bike." "I locked up my bike and secured my pet dog to the tree." I hope this helped you!