Contextual automatic speech recognition (ASR) with Speech-LLMs is typically trained with oracle conversation history, but relies on error-prone history at inference, causing a train-test mismatch in the context channel that we term contextual exposure bias. We propose a unified training framework to improve robustness under realistic histories: (i) Teacher Error Knowledge by using Whisper large-v3 hypotheses as training-time history, (ii) Context Dropout to regularize over-reliance on history, and (iii) Direct Preference Optimization (DPO) on curated failure cases. Experiments on TED-LIUM 3 (in-domain) and zero-shot LibriSpeech (out-of-domain) show consistent gains under predicted-history decoding. With a two-utterance history as context, SFT with Whisper hypotheses reduce WER from 5.59% (oracle-history training) to 5.47%, and DPO further improves to 5.17%. Under irrelevant-context attacks, DPO yields the smallest degradation (5.17% -> 5.63%), indicating improved robustness to misleading context. Our code and models are published on https://github.com/XYGuo1996/Contextual_Speech_LLMs.