h.s. is sometimes also seen abbreviated as "hs". i.e. is withour the fullstops.

hs = horis somni and half strength (the latter does not seem to apply here)

One mostly sees "at bedtime" and I have always used it as such.
However, here is one example where both are used, i.e. hs and at bedtime.

Patients and methods: Twenty-eight patients with previously untreated asymptomatic myeloma were treated with thalidomide 100 to 200 mg orally (PO) at bedtime (qhs) with serial increments of 50 to 100 mg at weekly intervals, as tolerated to a maximum of 600 mg PO qhs.
https://pubmed.ncbi.nlm.nih.gov/12506164/

(qhs = quaque hora somni = every bedtime or every night at bedtime)

Thalidomide BMS should be taken as a single dose at bedtime, to reduce the impact of somnolence. Capsules should not be opened or crushed (see section 6.6).
No specific dose adjustments are recommended for the elderly ≤ 75 years of age. For patients > 75 years of age, the thalidomide recommended starting dose is 100 mg per day.
https://www.medicines.org.uk/emc/product/6317

Due to the sedative effect associated with thalidomide, administration at bedtime is known to generally improve tolerability.
https://www.google.com/url?esrc=s&q=&rct=j&sa=U&url=https://...