How long do I have to wait after taking gabapentin to safely take hydrocodone?

If the same Dr. prescribed both medications, he/she is most likely to know these two medications have a major interaction when taken together and he/she outweighs the benefit of taken them is higher than the risk, your Dr. would not put you in harms way and he/she will monitor you closely.
Now if 2 different Drs. prescribed these medications without them knowing you are taking one or the other, I suggest you let them know.
Last but not least, if you are self medicating, I advice you to speak with your Dr. and follow his/her professional advice.