You are confusing yourself that E2 only occurs with a bulky base. That is not correct, we just often see it most with a bulky base. E2 will occur when we have a strong base, E1 when we have a weak base (as previous response says). However, E2 with a non-bulky strong base (like above) will give us the Zaitsev (more substituted) product, and a bulky strong base (like LDA or t-butoxide) gives us the Anti-Zaitsev (least substituted) product.
Chad has a really good video just on distringuishing between Sn2/Sn1 and E2/E1 which you should really check out.