Some corrections:
Honeybees do not reproduce asexually. The queens mate with one or more males and then make lots of other bees in a hive. The workers (females) do not reproduce at all (sexually or asexually.
I would be surprised if pillbugs were not sexual reproducers.
CostsBenefits of sexual reproduction:
Population reproduction rates can be higher using asexual reproduction. 100% of the population can lay eggs or have babies in a an asexual reproducing population. Only 50% in a sexually reproducing population (only the females).
This is also a benefit if a single animal colonized an isolated area. An asexual animal could reproduce by itself, a sexual one would not be able to unless already impregnated.
An energetic cost of the sexual reproductive method would involve the finding of a mate. This could also speed the process for asexual matings.
Environmental conditions favoring sexual or asexual reproduction:
Conditions favoring asexual reproduction would match up with its possible benefits (see above). Situations with low population density or isolated from possible mates.
Asexual reproduction would work best long term when there is not a lot of environmental variability (very stable) where new adaptations would be beneficial.
Sexual reproduction would be favored in cases were it would be beneficial for new gene combinations to be tested against different environmental conditions.
Clearly both have their potential beneficial uses.
Some species can do either depending upon their situation.
Some plants can reproduce sexually (often combined with dispersal to improve odds of survival) and at other times asexually (by runners for example), to make greater use of favorable local conditions.
Aphids can use a similar strategy, alternating sexual and asexual reproduction.
Some times, the mode of reproduction is tied to seasons, with different forms produced to better survive different or more variable conditions.