+1 to ltt
April and early may is not the time for tent camping other than for backcountry skiing and only if you have experience and gear for winter camping. You need a winter tent (NOT cheap), very warm sleeping bag, thick sleeping mat and lots of layers of down/fleece etc. Plus stove and lots of fuel for cooking and heating water. I've had subfreezing nights even in mid May up near Banff NP - and that was not at a very high elevation.
As mentioned, most campsites won't open until mid to late May - those that have early dates may be open but with no services and quite possibly no running water (water pumps are often not turned on until the risk of a freeze is over). If a campsite is shut for the winter, there may or may not be firewood in place yet for the summer.
Remember that in the mountains, April and May is not a time when you can really 'experience the outdoors' unless you are skiing, backcountry skiing or ice climbing. Seasonal roads will be shut, lakes still solidly frozen, higher elevations still snowy well into May and many if not most trails not hikeable. In a warmer spring, you may have some very low elevation hiking options in early May, but generally April and early May in the mountains are for end of season downshill skiing, backcountry skiing on the glaciers and resting up for the summer. Not hiking or walking.
If you want to explore the outdoors, you are best sticking with the coastal areas and lower elevation areas in the south of BC (Penticton etc). It will be warmer there with a lot more options for activities.
I would not suggest taking Greyhound across the country in mid April - not only would be it pretty boring (most of it would be white, flat and dreary), but you run a pretty high risk of encountering nasty weather. You could well end up with an unintended extra night or two somewhere in northern Ontario or the prairies. Flying would be much preferable, and a lot safer.
