I think the Bambino fits a lot into a pretty compact machine, making it great if you have limited space. As far as preground vs. fresh beans, I really think that you’ll be alright with just preground as long as you drink it fast enough. Especially if space is a concern, since an electric grinder takes up a pretty large amount of space. I’d say that if you’re comfortable going through the bag of beans in about a week, getting them preground at the shop is a totally fine option until you decide you want/need a grinder. This will vary based on your preferred roast level (darker roasts will offgas more quickly, which means their flavor will peak sooner, but also stale more quickly), but as long as you store it in an airtight container I’m sure this won’t have too much of an impact.
There is one excellent case for preground that might actually make the experience better: the quality of the grinder at the coffee shop. Even a basic shop should have a Mazzer Super Jolly, and a nice third-wave shop in the area will have a grinder that costs thousands. If you go through the coffee fast enough, these grinders will outperform any entry level grinder when it comes to espresso. You would only be missing out on the experience of dialing in a coffee, but I don’t think that’s necessarily worth the money it’d cost to buy a grinder. I’d explore the free option first, but once again I’d be more than happy to make some grinder recommendations if you’d like.