When I had no travel companions, I traveled alone several times.

Literal

Travel companions [subject-が] don't-exist time, alone [by-で] several-times traveled.

旅行仲間 (travel companions) is a compound with 仲間 (companion/buddy). 何度か (several times) uses the counter 度 with か for an approximate number. 一人で (alone) modifies the verb.