There's a variety of ways to approach this. Here's a few ideas that will hopefully inspire you to an answer:
gremlin> g = TinkerGraphFactory.createTinkerGraph()
==>tinkergraph[vertices:6 edges:6]
gremlin> g.V('name','marko').transform{[v:it,inE:it.inE().as('e').outV().as('v').select().toList(),outE:it.outE().as('e').inV().as('v').select().toList()]}
==>{v=v[1], inE=[], outE=[[e:e[9][1-created->3], v:v[3]], [e:e[7][1-knows->2], v:v[2]], [e:e[8][1-knows->4], v:v[4]]]}
The transform converts the incoming vertex to a Map and does internal traversal over in/out edges. You could also use path as follows to get a similar output:
gremlin> g.V('name','marko').transform{[v:it,inE:it.inE().outV().path().toList().toList(),outE:it.outE().inV().path().toList()]}
==>{v=v[1], inE=[], outE=[[v[1], e[9][1-created->3], v[3]], [v[1], e[7][1-knows->2], v[2]], [v[1], e[8][1-knows->4], v[4]]]}
I provided these answers using TinkerPop 2.x as that looked like what you were using as judged from the syntax. TinkerPop 3.x is now available and if you are just getting started, you should take a look at the latest that has to offer:
http://tinkerpop.incubator.apache.org/
Under 3.0 syntax you might do something like this:
gremlin> g.V().has('name','marko').as('a').bothE().bothV().where(neq('a')).path()
==>[v[1], e[9][1-created->3], v[3]]
==>[v[1], e[7][1-knows->2], v[2]]
==>[v[1], e[8][1-knows->4], v[4]]
I know that you wanted to know what the direction of the edge in the output but that's easy enough to detect on analysis of the path.
UPDATE: Here's the above query written with Daniel's suggestion of otherV usage:
gremlin> g.V().has('name','marko').bothE().otherV().path()
==>[v[1], e[9][1-created->3], v[3]]
==>[v[1], e[7][1-knows->2], v[2]]
==>[v[1], e[8][1-knows->4], v[4]]
To see the data from this you can use by() to pick apart each Path object - The extension to the above query applies valueMap to each piece of each Path:
gremlin> g.V().has('name','marko').bothE().otherV().path().by(__.valueMap(true))
==>[{label=person, name=[marko], id=1, age=[29]}, {label=created, weight=0.4, id=9}, {label=software, name=[lop], id=3, lang=[java]}]
==>[{label=person, name=[marko], id=1, age=[29]}, {label=knows, weight=0.5, id=7}, {label=person, name=[vadas], id=2, age=[27]}]
==>[{label=person, name=[marko], id=1, age=[29]}, {label=knows, weight=1.0, id=8}, {label=person, name=[josh], id=4, age=[32]}]