"However" functions as a more formal version of adverbial "though", this mainly due to an informal appeal to the reader that "though" suggests when it comes at the end of a sentence. On a different note, it doesn't always imply a direct contradiction. It could simply imply a qualification or contrast to what has already been stated.
For example, you could use it to qualify something to avoid confusion.
"I'm sick. I still would like to meet for coffee, though".
On the contrary, you could use it to contradict a previous statement.
"My boss told me not to come to work because I was sick. I had too much work to do to stay home, though".
In your example,
"How do we know it is a bicycle, though?"
might not (we'd need more context) contradict whether it is a bicycle or imply any contrast, but rather seek to qualify its bicycle-ness.
If you were compelled to change the wording, here are three options that incrementally emphasize the qualification:
"It is a bicycle, but how do we know it is a bicycle?"
"It is a bicycle, yet how do we know it is a bicycle?"
"It is a bicycle; however, how do we know that it is a bicycle?"