I lost my front tooth bridge. My teeth are really short and I have decay. Will my dentist be able to fix them?

If the roots are strong your dentist should be able to save the teeth and restore without much difficulty.  You may require crown lengthening or root canals but one visit should give instant improvement.

Even if your bridge can be re-cemented, it's unlikely to fit properly other than as a temporary solution. It's usually best to keep as many of your natural teeth as possible, but sometimes teeth are so badly broken down and/or infected that it doesn't make much sense to keep them. Implants could be the least expensive and most reliable option for you long term. The best first step for you is to see a dentist for a complete examination with x-rays. That's the only way to find out what's really going on in your mouth and what your options actually are.

By your description is sounds as if you will most likely not be able to reuse the bridge and would require the broken teeth to be removed.    If you have other teeth that could be utilized as a bridge anchor (or abutment), then possibly another longer span type of bridge may be able to be fabricated for you.  Other options are dental implants (possibly the best way to go) or a removable partial denture.If you have a history of much decay and don't have great oral hygiene and your teeth are in poor shape, many times it's best to "just punt" and have the bad teeth removed and proceed with one of the options I just mentioned.  I would suggest that you not spend a lot of money on "heroic" dentistry that may not last.