What I would do is use data for Win 231 powder. W231 and HP-38 are essentially the same powder - come from same company (St Marks Powder, formerly Primex) and delivered to Winchester and Hodgdon for them to package and sell. W231 data is much more common in the manuals than HP-38.
Important - always back off 10% when changing any component.
It is an accepted practice to use load data for the next higher weight bullet of the same type (jacketed vs jacketed, lead vs lead, etc.) That is, as long as the next higher weight is within a reasonable range. Therefore, using Speer data for their jacketed 185 gr Gold Dot and W231 and allowing for a 10% decrease the min/max load would be 5.9 to 6.6 grains of HP-38.
That's where I would start. You can most likely go a little higher in powder weight, but only in increments looking for any signs of excessive pressure along the way.
You can use the same procedure with Bullseye, but in my book, W231/HP-38 are a little more forgiving of going overboard than is the faster rated Bullseye.