How many bands do you get with single digest with either BamH1 or Nde1? With both, based on pET15b sequence you should get a small and probably undetectable 12bp fragment and the rest of your plasmid (single band). Can you post a picture of your gel? A possibility is that you have partial digest. You need to add BSA to Buffer 3 for BamH1 to digest properly. No BSA, no good cut from BamH1

You can start with NdeI in buffer 2 and when the DNA is digested then you can add BamHI in  digested DNA. I think no need of gel extraction. I am also agree with Mesplède that you should add BSA to Buffer 3 for BamHI digestion. As you know BamHI have the star activity so it might be a cause of this problem. You can also check the efficacy of  2X tango buffer. AND good luck for this chance

Digest your product with  Nde I with buffer 3.1. after digestion with NdeI add Bam HI in same vial for further digestion with Bam HI.

P.S: In Buffer 3.1 there is no star activity for Bam HI and Nde I.

How old is your Bamh1?  Old enzyme will have star activity, regardless of the buffer used. 

I accept above suggestion to overcome two more bands in gel instead of one. I hope you have also checked the restriction site in your desired sequnce!!!! some time the restriction site within your seq have chance to cleave the desired DNA.

Or your constuct may be contaminated!!!!

Did you got clear band of pET vector

All the best

does bamh1 have star activity