The BEDOPS suite includes bedops, a utility which performs various set operations on BED inputs. It's not clear if this would solve your specific problem, but you can specify the degree of overlap as criteria for inclusion, when using the --element-of operator with bedops.

For example, the following command would return elements from Reads.bed which overlap elements in Map.bed by 80% or more of segment length:

$ bedops --element-of -80% Reads.bed Map.bed