given an undirected, unweighted graph and a vertex v, I want to compute
the k-disk around v, i.e. the induced subgraph of vertices at a distanst
at most k from v.

Of course, this can be easily be done by a variation of BFS or DFS. Is
it possible do use graph_tool.search.bfs_search in some way for this?

This will work. But doesn't it first compute the shortest distance from
v to all other vertices in g and then applies a filter? This is rather
inefficient, especially when then graph is huge...