The bisphophonate Aldronate reduces height.  Other bisphophantes such as zoledronate have an impact on the growth plate and may have an impact on height.  I don’t know for sure what affect bisphophonates have on height but if I had to guess I would say that they result in decreased height.

Effect of Bisphosphonates on the Rapidly Growing Male Murine Skeleton

“C57Bl6/J male mice were treated from 18 to 38 days of age with vehicle, alendronate, pamidronate, zoledronate or clodronate at doses selected to replicate those used in humans. Treatment with alendronate, pamidronate and zoledronate, but not clodronate led to a decrease in the number of chondrocytes per column in the hypertrophic chondrocyte layer. This was not associated with altered hypertrophic chondrocyte apoptosis or vascular invasion at the growth plate.

The effects of pamidronate on trabecular microarchitecture were less beneficial than those of alendronate and zoledronate. Pamidronate did not increase cortical thickness or cortical area/total area relative to control mice. These studies suggest that bisphosphonate administration does not adversely affect skeletal growth.”

“Technicium, 99mTc-labeled 1-hydroxy-methyledene bisphosphonate, a compound closely related to clodronate, is used for bone scans. In children and growing animals, this agent is avidly taken up in the region of the growth plate where cartilage is being replaced by bone”

“first generation bisphosphonates (ethane-1-hydroxy-1,1-diphosphonate and dichloromethylene diphsophonate), performed in growing rats more than four decades ago, demonstrated expansion of the growth plate and persistence of columns of calcified cartilage”<-note that expansion of the growth plate does not always lead to increased height.

“Pamidronate decreases basal ERK1/2 phosphorylation in hypertrophic chondrocytes”<-other bisphosphonates did not alter ERK1/2 phosphorylation.

“Treatment of hypertrophic chondrocytes with phosphate leads to rapid phosphorylation of Erk1/2 which is required for phosphate-mediated hypertrophic chondrocyte apoptosis”

“Bisphosphonates do not impair hypertrophic chondrocyte apoptosis in vivo”<-although the pamidronate group had a slight increase in hypertrophic chondrocyte apoptosis.

“zoledronate suppresses MMP-9 expression, whereas pamidronate increases MMP-9 mRNA
levels in cells of the monocyte/macrophage lineage, and clodronate has no effect”

“The number of osteoclasts in this region [metaphysis] (350 microns) was significantly decreased in the mice treated with alendronate and zoledronate relative to control mice (2.3  and 3.3 respectively vs 7.5 in control mice). Pamidronate and clodronate treatment resulted in a small and insignificant decrease in cortical osteoclasts in this region relative to control animals (6.0 and 7.0 respectively).”

“Femoral length did not differ between control and treated mice, nor among treatment groups(data not shown).”<-This is unfortunate as any non-signficiant difference in femur length could be notable.

“the non-nitrogen containing bisphosphonate, clodronate, did not alter the number of hypertrophic chondrocytes per column and led to fewer growth plate changes than the nitrogen-containing bisphosphonates.”