I have a typical Asian big nose as well as a pretty flat bridge. What can be done to enhance my nose? (photo)

I do agree that your nose will have a more attractive profile and greater refinement from frontal view with some bridge augmentation.  I would strongly recommend using tissue from your own body as this will create the safest, permanent and I feel, the most attractive result.  Silicone is less than ideal for its temporary nature, high risk of complications, and un-natural contours it can create over time.  By building up and projecting and refining the tip and bridge of your nose, you will be able to achieve the look you seek without shaving the nasal bones.  

With thick skin like yours, definition and refinement may be created by increasing the projection of the nose.  Dorsal augmentation may be accomplished by artificial material such as silicone, but I prefer to use material from the patient's own body, usually rib cartilage for this type of procedure.  I believe this leads to a more natural appearance, a less mobile bridge, and reduced risk of infection or extrusion.  The tip could be improved with some projection and narrowing of the tip cartilages and reduction of the nostril flare (alar base reduction).  I doubt any bone reduction would be needed.My educational video linked below may provide additional helpful information.

Your bridge may be narrowed and augmented with a graft and the tip of your nose may be enhanced, which would narrow the nostrils. However, you should meet with an experienced board certified plastic surgeon for a better assessment. Your nose has be viewed in relation to the rest of your face to make it as harmoniously proportionate as desired.

A low, wide bridge and an underprojected, round tip are common features of the Asian nose.  Patients often request a higher, more narrow bridge and a more refined tip.  These changes are best accomplished by grafting the nasal bridge and tip. Silicone implants can be used to raise the bridge, and silicone "L-strut" implants are used throughout the world as a quick, simple way to reshape the Asian nose.  I personally prefer using a patient's own rib cartilage since the amount of septal cartilage is often insufficient.  It is safer the silicone in the long run due to less risk of infection or extrusion.  

It looks like you need a dorsal augmentation and as you said maybe a tip procedure or a graft. Best to be seen in person. Good luck.