H Street is commonly used by bicyclists leaving Sacramento Valley Station, and others as well. It has decent bicycle facilities except for some gaps.
H Street has a bike lane on the south side from 5th Street to 16th St, except one block, 7th Street to 8th Street. There is absolutely no reason for this gap. This is the section between the Sacramento County Administration Building on the south and a decked parking garage on the north. The parking seems to be there for the convenience of people working in the building, as there does not seem to be turnover of the parking spots. There is ample parking in the garage. This parking should be removed and a bike lane painted IMMEDIATELY. No excuses. A common quote in the bicyclist community is “sharrows are bullshit”, and this is the case here, where the city has preferenced motor vehicle drivers over bicyclist safety.

There is a bike lane on the north side between 7th Street and 13th Street. Bike lanes on the left side of one-way streets are much less used than right side bike lanes, but are useful.
H Street might also be used inbound to SVS if it were converted to a two-way street. When the city completes the installation of a separated bikeway on I Street westbound between 21st Street and 12th Street, inbound access to SVS will be improved, but the project stops well short of the station, leaving the seven blocks to 5th Street with only a bike lane, with hazardous parking in the part-time bike lane in the block of 7th Street to 6th Street at the county jail. So having H Street as an inbound would still be very useful. Eventually F Street can also provide for inbound, but only when the station access point is opened and if bike facilities are installed on F Street. Every street with significant traffic volume should have bicycle facilities.
There are four curb extensions (bulb-outs) on the south side of the street, at 9th St southeast corner, 10th Street southwest and southeast corners, and 14th Street southwest corner. Curb extensions are of clear benefit for walkers, reducing crossing distance and improving visibility. However, unless removed, they would prevent the installation of a parking protected separated bikeway on the south side of H Street. There are not curb extensions on the north side. If these four curb extensions remain, then every corner should receive this treatment, initially with paint and post extensions, then with concrete extensions.
If H Street were converted from one-way to two-way, the section between 8th Street and 16th Street would be easy. Signalized intersections at 8th, 9th, 10th, 12th, 15th, and 16th would need to be changed, but otherwise there would be no significant cost or work. The street would be restripesd, but on the same pattern.
The challenge is between 5th Street and 8th Street, where H Street carries light rail tracks. From 7th Street to 8th Street, the westbound track from 8th Street is on the north side of the street. From 6th Street to 7th Street, the eastbound track to 7th Street splits off. The angle of the tracks here would present a safety hazard for bicyclists, so some sort of special accommodation for crossing the tracks would be needed, perhaps a painted bike lane that crosses the tracks at a higher angle. From 5th Street to 6th Street, there is again a single track on the north side. It might be possible to fit in an inbound (westbound) bike lane in these three blocks. See the Streetmix diagram below, however, the measurements are from Google Maps, not from on-the-ground measurements, so may be inaccurate.
However, as a transit supporter, I must point out that light rail should be double-tracked from 7th Street to 5th Street, and if this were done, there would not be space for a a bike lane on the north. This alignment will be used in the future for light rail through SVS and continuing to the River District (rather than on 7th Street), so a single-track segment is not appropriate. The city, who is responsible for SVS, has offered in the Sacramento Valley Station Master Plan, the following diagram, but this is within SVS west of 5th Street. So far as is known, SacRT does not have a design for light rail between 5th Street and 8th Street.

There are two completely unnecessary signalized intersections in this stretch, at 11th Street and at 14th Street. Neither of these cross-streets has enough traffic to justify a traffic signal. These should be removed, whether or not the street becomes two-way, and if it does, the equipment can be used to reduce the cost of the conversion by being used at other intersections.
There was a proposal to move light rail from K Street to H Street, between 12th Street and 8th Street, part of the streetcar project, removing light rail from K Street to that it could better be used for streetcar. However, this proposal is dead, so far as is known, since the streetcar now has a completely different and much reduced alignment.
Summary: H Street can be made immediately safer for bicyclists by removing parking 7th to 8th Streets. Safety and access to Sacramento Valley Station can be improved with other actions.