Would alar base reduction be useless without doing some work with the nose bridge as well?

Every nose is
different and unique to that individual. If the appearance of your nose
concerns you enough to do something about it, it can be improved with a natural
artistically performed rhinoplasty. What would be the best option and exact
procedure (alar base reduction alone or full rhinoplasty) would depend on an in person examination (not just an online
consultation) and discussion about desired outcome.
Keep in mind that following advice from a surgeon on this or any other website
who proposes to tell you exactly what to do and how technically to do
it based on two dimensional photos without examining you, physically
feeling your tissue, assessing your desired outcome, taking a full medical
history and discussing the pros and cons of the operative procedure would not
be in your best interest. Natural appearing results need to be individualized
and what is appropriate for one patient is not necessarily the best for someone
else. I would suggest that you find a surgeon with extensive rhinoplasty
experience certified by the American Board of Plastic Surgery and one who is
ideally a member of The American Society for Aesthetic Plastic Surgery (ASAPS) or facial plastic surgeon (otolaryngologist)  that you trust and are comfortable with. You should discuss your concerns with that
surgeon in person.
Robert Singer, M.D., FACS
La Jolla, California

Dear santalos5,it is hard to tell without an examination. I would suggest you to consult a board-certified plastic surgeon. Only after a thorough examination you will get more information and recommendations.Daniel Barrett, MD, MHA, MS 
Certified, American Board of Plastic Surgery  
Member, Am. Society of Plastic Surgery