From what I can tell, the Hellenic Bosporan Kingdom never managed to extend its control beyond the southernmost portion of the Crimean peninsula for any significant length of time. Even when they did, they fell far short of the isthmus of Perekop. Had they secured this strategically invaluable land bridge, surely they would have been able to expand their cities on the coast and develop the interior of the peninsula for agriculture without hindrance from raiding nomads from the north? They would have at least been better protected from the invading Huns and Goths that ultimately wiped them out in the 4th century.
Why were they never able to push further north? Considering they were an advanced Hellenic civilisation, at least compared to the disunited nomads they had to contend with in the surrounding lands, I assume they would have at least had the means to accomplish this had they tried? Surely the Romans would have had a strategic interest in expanding up to the isthmus of Perekop to secure their northernmost dominion from attack once the Bosporan Kingdom had become their client state?
This isn't so much as a direct answer to your question as a clarification of your premise that lies in the geography of the area. You state that the isthmus of Perekop was a strategically invaluable land bridge that would have secured the peninsula. The problem with that is that in realty Crimea could be attacked from a number of directions. The Sea of Azov, and especially the Sivash area (east of the isthmus) are extremely shallow. In some places, the depth is less than a meter. It can be easily crossed using rafts or small boats, or even forded in some places. Secondly, it freezes in the winter, meaning an invading army could march on foot. Thus to control the peninsula, one would have to be able to defend a much larger perimeter than just the isthmus.
Secondly, and this might be a partial answer to your question, is that the climate of Crimea is VERY different between the southern coast and the remaining part. The coast is protected from northern winds by the Crimean mountains. South of the mountains, the climate is mild, Mediterranean - a version of the climate that the Greeks and the Romans would have been used to. North of the mountains, the climate is much harsher, more similar to that of the Pontic steppe, with colder winters and less precipitation. Without irrigation (which really only became possible in the 20th century with the completion of the North-Crimean canal), agriculture is difficult and risky. Thus there wasn't much value in controlling that area.