Laser Hair Removal on Nose Bridge?

Without examining your skin with a good light and magnification, it would be difficult to say why the hair redness exists. Some people develop seborrheic dermatitis between the eyebrows and the redness is accompanied by some scaling of greasy yellow to white skin. If the redness is only located in the pores of the hairs, then it is not seborrhea. See a dermatologist to get the correct diagnosis. There may be a simple solution to make your skin better.

It can be safely removed with laser. The redness is unlikely to be related to it. You should get the laser hair removal during cold winter months so sun exposure is not an issue. The sun exposure can increase the redness after the laser.
In the meantime start wearing sunscreen on the nose every day and see a dermatologist to see if you have rosacea or some other condition.
Regards

Laser hair removal is an effective form of "hair reduction" on the body and the nose is no exception. Laser hair removal is most effective when treating dark hairs set against fair skin.
The redness you describe has nothing to do with hair growth or presence. There are a number of reasons and causes of redness on the nose. A few of the most common causes are Seborrhea, Rosacea or telangiectasias (blood vessels).