Bst DNA polymerase are commonly used in LAMP because they have strong strand displacement activity (required in isothermal techniques). However most of this polymerase are really unstable above 70°C, so it is impossible to use them in a pre-denaturation steps where temperatures are close to 90 °C.
Well for each PCR cycle you need to Denature the DNA. This first step of every cycle requires high temperature to denature the dsDNA. This temperature usually goes between 92-94°C.
If you just run the PCR at 70°C to maintain the stability of the Bst polymerase I highly doubt you will get any PCR product, as you don't denature DNA at 70°C (i think it is established that all DNA denatures at 90 - 95°C). You would just be annealing and extending nothing.
I have never used Bst before, but after reading up on LAMP for my own research, I don't see why you can't use it. If you add betaine to the reaction (as you would in LAMP), the DNA should be a mixture of ss and ds at 70C, because betaine hase the effect of strongly reducing the melting temperature of the DNA. I can't imagine that your reaction would be as robust as it might be with Taq, but I would think you should still see some amplification using standard primers (especially if they are long enough to anneal nicely at 70C).