Here is an interesting discussion of US versus U.S. versus USA versus U.S.A. from Wikipedia: Manual of Style:
In American and Canadian English, U.S. (with periods) is the dominant abbreviation for United States. US (without periods) is more common in most other national forms of English. Some major American guides to style, such as The Chicago Manual of Style (16th ed.), now deprecate U.S. and prefer US. Use of periods for abbreviations and acronyms should be consistent within any given article, and congruent with the variety of English used by that article. In longer abbreviations (three letters or more) incorporating the country's initials (USN, USAF), do not use periods. When the United States is mentioned with one or more other countries in the same sentence, U.S. or US may be too informal, especially at the first mention or as a noun instead of an adjective (France and the United States, not France and the U.S.). Do not use the spaced U. S., nor the archaic U.S. of A., except when quoting. Do not use U.S.A. or USA, except in a quotation or as part of a proper name (Team USA), as these abbreviations are also used for United States Army and other names.
The Chicago Manual of Style, 15th Edition (2003) comes out strongly in favor of spelling out United States (rather than abbreviating it) when the term is used as a noun and not an adjective:
15.34 "U.S." or "US." Except in scientific style, U.S. traditionally appears with periods. Periods may nonetheless be omitted in most contexts, Writers and editors need to weight tradition against consistency. In running text, the abbreviation (in either form) is permissible when used as an adjective, but United States as a noun should be spelled out.
Words Into Type, Third Edition (1974) takes an even stronger anti-abbreviation position:
In the most formal writing, United States should always be spelled out; in other works U.S. is gaining currency as an adjective when preceding a government agency, department or organization or the name of a government vessel. [Examples omitted.] When used as an adjective with general terms, United States should be spelled out. [Examples omitted.]
Both Chicago and Words Into Type have so little regard for USA that they don't even mention it as an option in their discussions of abbreviations for countries.
The Associated Press Stylebook (2006), however, accepts both U.S. and USA as nouns, and seemingly views them as equally valid designations:
U.S. The abbreviation is acceptable as a noun or adjective for Unites States.
USA No periods in the abbreviated form for United States of America.
Nevertheless, I have never seen a style guide that approved of using USA as an adjective.
Update (June 23, 2017): More on 'U.S.' vs. 'US'
Having belatedly acquired the 16th edition of the Chicago Manual of Style (2010), I should note that it has substantially altered its views on the use of U.S. versus US from what they were seven years earlier (see above). The updated advice appears in three sections:
10.4 Periods with abbreviations. ...
Use no periods with abbreviations that appear in full capitals, whether two letters or more and even if lowercase letters appear within the abbreviation: VP, CEO, MA, MD, PhD, UK, US, NY, IL (but see rule 4).
In publications using traditional state abbreviations, use periods to abbreviate United States and its states and territories: U.S., N.Y., Ill. Note however, that Chicago recommends using the two-letter postal codes (and therefore US) wherever abbreviations are used; see 10.28.
...
10.28 US states and territories. In running text, the names of states, territories and possessions of the United States should always be spelled out when standing alone and preferably (except for DC) when following the name of a city: [example omitted]. In bibliographies, tabular matter, lists, and mailing addresses, they are usually abbreviated. In all such contexts, Chicago prefers the two-letter postal codes to the conventional abbreviations.
...
10.33 "US" versus United States. In running text, spell out United States as a noun; reserve US for the adjective form only (in which position the abbreviation is generally preferred.) See also 10.4.
So the current guideline seems to advocate using U.S. if you use "traditional" state abbreviations (like N.Y. and Ill.) but to use US if you use postal-code-style abbreviations (like NY and IL)—which Chicago now prefers. But there's no telling what the 17th edition will recommend when it appears in the next year or two. Recently a publisher at which I regularly do freelance editing switched to using US in running text whether the term is functioning as an adjective or as a noun.
Best Answer
"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.
On the contrary, you could use it to contradict a previous statement.
In your example,
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: