Relevent experience for an MBA in Oil & Gas refers to professional experience that is either directly related to Oil & Gas or in close relation. Whether it be upstream, midstream, downstream or in a related side sector, the key is having held a managerial role or showing managerial potential.
Your BSc in Environemental Science is definitely in the right direction in terms of education. On the relevance of your professional experience, it would depend the supervisory elements and specificities of the job role (i.e. how relevant is it to the oil & gas industry). Entry requirements vary by university so of course, you should enquire to admissions departments individually to be sure of each university's standards.
How many years of professional experience do you have?
For program ideas, here are some MBA programs in Energy & Sustainabililty.
Best of Luck,