Here is a fairly simple (and hopefully readable) native Python solution. It assumes that the bed file is sorted prior to parsing:

from itertools import groupby

class BedRecord(object):
    def __init__(self, chr, start, end, feature):
        self.chr = chr
        self.start = start
        self.end = end
        self.feature = feature

def parse_records(in_file):
    with open(in_file) as f:
        for line in f:
            yield BedRecord(*line.strip().split())

def merge_groups(group):
    prev = next(group)
    output = [prev]
    for record in group:
        if record.start <= prev.end:
            output[-1].end = max(output[-1].end, record.end)
        else:
            output.append(record)
    return output

def main(in_file):
    for _, group in groupby(parse_records(in_file), lambda x: (x.chr, x.feature)):
        for r in merge_groups(group):
            print('\t'.join([r.chr, r.start, r.end, r.feature]))

if __name__ == '__main__':
    main('test.bed')

Here is a fairly simple (and hopefully readable) native Python solution. It assumes that the bed file is sorted prior to parsing:

from itertools import groupby

class BedRecord(object):
    def __init__(self, chr, start, end, feature):
        self.chr = chr
        self.start = start
        self.end = end
        self.feature = feature

def parse_records(in_file):
    with open(in_file) as f:
        for line in f:
            yield BedRecord(*line.strip().split())

def merge_groups(group):
    output = [next(group)]
    for record in group:
        if record.start <= output[-1].end:
            output[-1].end = max(output[-1].end, record.end)
        else:
            output.append(record)
    return output

def main(in_file):
    for _, group in groupby(parse_records(in_file), lambda x: (x.chr, x.feature)):
        for r in merge_groups(group):
            print('\t'.join([r.chr, r.start, r.end, r.feature]))

if __name__ == '__main__':
    main('test.bed')