Permanent and Quick Option for Teeth Gap?

I am afraid that dental bonding will not be a good option for your to close the gap between your front teeth.   A 3mm space is fairly large and attempting dental bonding to close the space will make your front two teeth look much too wide.  A much better approach would be to place two porcelain veneers.  By doing veneers you give the laboratory the freedom to close the space without making them appear as wide.  In addition, the lab can match the color of the existing teeth through digital shade imaging.  This process will only take two visits and give you a MUCH better result.  

Teeth effect bands should be avoided, as they potentially can migrate to the roots and extract the teeth! These have been marketed by non dentists to be used by non dentists (you) and thus are not supervised by a dentist.
As the teeth move, the bands go deeper (towards the nose on the upper teeth). Since they act slowly, the damage they do is hard to notice at first, but the action CAN be fast enough to do severe irreversible damage before one can be seen by a dentist to "save the day".
Bonding might work, so I would encourage a visit with an experienced dentist. It is not a simple process if you want them to look natural, so experience and training matters.

Bonding is always a great, quick, long-term and economical option.  Unless the clinician is highly skilled, I would suggest a "wax-up" or prototype model of your proposed outcome prior to treatment.  This way a guide can be produced to transfer that to your teeth.  It will show correct proportions of your teeth:  length and width.  A general rule of thumb is the width of the front teeth should be approximately 75-80% of the length.  So if a tooth is 10 mm long, it should be about 7.5 - 8 mm wide.  It will also take into account the way your upper and lower teeth come together, bite and chew which will ultimately make the longevity more predictable.  You may also want to consider optional teeth whitening prior to bonding to enhance the result - keep in mind the color of the bonding will stay the same if you decide to whiten in the future.  Not much about "tooth effect bands" to show their efficacy and post-stability.  Good luck!

Bonding the teeth to disguise the gap between them is a good option in some cases. You want to make sure that your teeth are the right proportions to accommodate this gap. By that, I mean that if you already have short teeth or wide teeth, adding bonding to the sides to close the gap will only make them look shorter and wider (and unnatural). Keep in mind that bonding is a good option that will last you but can discolor over time due to the nature of the material used. Another option that is much longer lasting would be to get porcelain veneers on these teeth, if you are a candidate. 
With regard to the bands you mentioned, I would never recommend a patient to do any sort of orthodontic treatment (moving the teeth with bands, for example) at home. It can damage the teeth. Even if you were to do it at home and were able to move the teeth, the space that was once between those teeth will just be transferred to the sides of them, so you will still have a space. Also, Once you take the band off, the teeth will drift back to their normal position if they are not being retained. Hope this helps!

A 3mm wide space between your front teeth is a great candidate for dental bonding as long as your teeth are long enough to accommodate the added width. If you start out with short teeth with a 3mm gap, then trying to widen the teeth will make your front teeth look too wide. Dental bonding is the most conservative procedure we do as dentists and it can last for many many years, but no procedures are predictably permanent. Certainly stay away from do it yourself orthodontics!