I had an interesting journey back from Bromley one evening where the guard and I discussed how difficult a connection this was. The best we could come up with was Bromley to Catford and then bus (185?) to forest hill (I was doing the return bit as part of a journey from somewhere in Kent). Definitely less than an hour if your train times match up.

I think I've also done the crofton park route but less good bus connections to/fromwest forest hill.